diff --git a/templates/zerver/api/mute-topics.md b/templates/zerver/api/mute-topics.md
new file mode 100644
index 0000000000..44226ce82a
--- /dev/null
+++ b/templates/zerver/api/mute-topics.md
@@ -0,0 +1,61 @@
+# Topic muting
+
+This endpoint mutes/unmutes a topic within a stream that the current
+user is subscribed to.  Muted topics are displayed faded in the Zulip
+UI, and are not included in the user's unread count totals.
+
+`PATCH {{ api_url }}/v1/users/me/subscriptions/muted_topics`
+
+## Usage examples
+
+<div class="code-section" markdown="1">
+<ul class="nav">
+<li data-language="python">Python</li>
+<li data-language="curl">curl</li>
+</ul>
+<div class="blocks">
+
+<div data-language="curl" markdown="1">
+
+```
+curl -X PATCH {{ api_url }}/v1/users/me/subscriptions/muted_topics \
+    -u BOT_EMAIL_ADDRESS:BOT_API_KEY \
+    -d "stream=Verona"
+    -d "topic=dinner"
+    -d "op=add"
+```
+
+</div>
+
+<div data-language="python" markdown="1">
+
+{generate_code_example(python)|/users/me/subscriptions/muted_topics:patch|example}
+
+</div>
+
+</div>
+
+</div>
+
+## Arguments
+
+{generate_api_arguments_table|zulip.yaml|/users/me/subscriptions/muted_topics:patch}
+
+## Response
+
+#### Example response
+
+A typical successful JSON response may look like:
+
+{generate_code_example|/users/me/subscriptions/muted_topics:patch|fixture(200)}
+
+
+An example JSON response for when an `add` operation is requested for a topic
+that has already been muted:
+
+{generate_code_example|/users/me/subscriptions/muted_topics:patch|fixture(400_topic_already_muted)}
+
+An example JSON response for when a `remove` operation is requested for a
+topic that had not been previously muted:
+
+{generate_code_example|/users/me/subscriptions/muted_topics:patch|fixture(400_topic_not_muted)}
diff --git a/templates/zerver/help/include/rest-endpoints.md b/templates/zerver/help/include/rest-endpoints.md
index a6c861c065..8ce18de740 100644
--- a/templates/zerver/help/include/rest-endpoints.md
+++ b/templates/zerver/help/include/rest-endpoints.md
@@ -13,6 +13,7 @@
 * [Add subscriptions](/api/add-subscriptions)
 * [Remove subscriptions](/api/remove-subscriptions)
 * [Get topics in a stream](/api/get-stream-topics)
+* [Topic muting](/api/mute-topics)
 * [Create a stream](/api/create-stream)
 * [Get stream ID](/api/get-stream-id)
 
diff --git a/zerver/lib/api_test_helpers.py b/zerver/lib/api_test_helpers.py
index b585c6d65f..c9e244eb14 100644
--- a/zerver/lib/api_test_helpers.py
+++ b/zerver/lib/api_test_helpers.py
@@ -267,6 +267,50 @@ def remove_subscriptions(client):
     validate_against_openapi_schema(result, '/users/me/subscriptions',
                                     'delete', '200')
 
+def toggle_mute_topic(client):
+    # type: (Client) -> None
+
+    # Send a test message
+    message = {
+        'type': 'stream',
+        'to': 'Denmark',
+        'subject': 'boat party'
+    }
+    client.call_endpoint(
+        url='messages',
+        method='POST',
+        request=message
+    )
+
+    # {code_example|start}
+    # Mute the topic "boat party" in the stream "Denmark"
+    request = {
+        'stream': 'Denmark',
+        'topic': 'boat party',
+        'op': 'add'
+    }
+    result = client.mute_topic(request)
+    # {code_example|end}
+
+    validate_against_openapi_schema(result,
+                                    '/users/me/subscriptions/muted_topics',
+                                    'patch', '200')
+
+    # {code_example|start}
+    # Unmute the topic "boat party" in the stream "Denmark"
+    request = {
+        'stream': 'Denmark',
+        'topic': 'boat party',
+        'op': 'remove'
+    }
+
+    result = client.mute_topic(request)
+    # {code_example|end}
+
+    validate_against_openapi_schema(result,
+                                    '/users/me/subscriptions/muted_topics',
+                                    'patch', '200')
+
 def render_message(client):
     # type: (Client) -> None
 
@@ -513,6 +557,7 @@ TEST_FUNCTIONS = {
     'get-profile': get_profile,
     'add-subscriptions': add_subscriptions,
     '/users/me/subscriptions:delete': remove_subscriptions,
+    '/users/me/subscriptions/muted_topics:patch': toggle_mute_topic,
     '/users:get': get_members,
     '/realm/filters:post': add_realm_filter,
     '/register:post': register_queue,
@@ -600,6 +645,7 @@ def test_streams(client, nonadmin_client):
     get_streams(client)
     get_subscribers(client)
     remove_subscriptions(client)
+    toggle_mute_topic(client)
     get_stream_topics(client, 1)
 
     test_user_not_authorized_error(nonadmin_client)
diff --git a/zerver/openapi/zulip.yaml b/zerver/openapi/zulip.yaml
index 59acfd49d3..a39be55d64 100644
--- a/zerver/openapi/zulip.yaml
+++ b/zerver/openapi/zulip.yaml
@@ -790,6 +790,71 @@ paths:
             application/json:
               schema:
                 $ref: '#/components/schemas/NonExistingStreamError'
+  /users/me/subscriptions/muted_topics:
+    patch:
+      description: Toggle muting for a specific topic the user is subscribed
+        to.
+      parameters:
+      - name: stream
+        in: query_function
+        description: The name of the stream in which to mute the topic.
+        schema:
+          type: string
+        example: Verona
+        required: true
+      - name: topic
+        in: query
+        description: The topic to (un)mute. Note that the request will succeed
+          regardless of whether any messages have been sent to the
+          specified topic.
+        schema:
+          type: string
+        example: dinner
+        required: true
+      - name: op
+        in: query
+        description: Whether to mute (`add`) or unmute (`remove`) the provided
+          topic.
+        schema:
+          type: string
+          enum:
+          - add
+          - remove
+        example: add
+        required: true
+      security:
+      - basicAuth: []
+      responses:
+        '200':
+          description: Success.
+          content:
+            application/json:
+              schema:
+                $ref: '#/components/schemas/JsonSuccess'
+        '400_topic_already_muted':
+          description: Bad request.
+          content:
+            application/json:
+              schema:
+                allOf:
+                  - $ref: '#/components/schemas/JsonError'
+                  - example:
+                      {
+                          "msg": "Topic already muted",
+                          "result": "error"
+                      }
+        '400_topic_not_muted':
+          description: Bad request.
+          content:
+            application/json:
+              schema:
+                allOf:
+                  - $ref: '#/components/schemas/JsonError'
+                  - example:
+                      {
+                          "msg": "Topic is not there in the muted_topics list",
+                          "result": "error"
+                      }
   /realm/filters:
     post:
       description: Establish patterns in the messages that should be