Index: src/wp-includes/rest-api/endpoints/class-wp-rest-taxonomies-controller.php
===================================================================
--- src/wp-includes/rest-api/endpoints/class-wp-rest-taxonomies-controller.php	(revision 39069)
+++ src/wp-includes/rest-api/endpoints/class-wp-rest-taxonomies-controller.php	(working copy)
@@ -197,7 +197,7 @@
 		$response = rest_ensure_response( $data );
 
 		$base = ! empty( $taxonomy->rest_base ) ? $taxonomy->rest_base : $taxonomy->name;
-		$response->add_links( array(
+		$links = array(
 			'collection'                => array(
 				'href'                  => rest_url( sprintf( '%s/%s', $this->namespace, $this->rest_base ) ),
 			),
@@ -204,8 +204,30 @@
 			'https://api.w.org/items'   => array(
 				'href'                  => rest_url( sprintf( 'wp/v2/%s', $base ) ),
 			),
-		) );
+		);
 
+		$post_type_links = array();
+		foreach ( $taxonomy->object_type as $type ) {
+			$post_type_object = get_post_type_object( $type );
+
+			// Skip post types that are not public.
+			if ( empty( $post_type_object->show_in_rest ) ) {
+				continue;
+			}
+
+			$rest_base = ! empty( $post_type_object->rest_base ) ? $post_type_object->rest_base : $post_type_object->name;
+			$post_type_links[] = array(
+				'href'      => rest_url( 'wp/v2/' . $rest_base ),
+				'post_type' => $type,
+			);
+		}
+
+		if ( ! empty( $post_type_links ) ) {
+			$links['https://api.w.org/post_type'] = $post_type_links;
+		}
+
+		$response->add_links( $links );
+
 		/**
 		 * Filters a taxonomy returned from the REST API.
 		 *
Index: tests/phpunit/tests/rest-api/rest-taxonomies-controller.php
===================================================================
--- tests/phpunit/tests/rest-api/rest-taxonomies-controller.php	(revision 39069)
+++ tests/phpunit/tests/rest-api/rest-taxonomies-controller.php	(working copy)
@@ -170,6 +170,8 @@
 		$this->assertEquals( $tax_obj->hierarchical, $data['hierarchical'] );
 		$this->assertEquals( rest_url( 'wp/v2/taxonomies' ), $links['collection'][0]['href'] );
 		$this->assertArrayHasKey( 'https://api.w.org/items', $links );
+		$this->assertArrayHasKey( 'https://api.w.org/post_type', $links );
+		$this->assertEquals( rest_url( 'wp/v2/posts' ), $links['https://api.w.org/post_type'][0]['href'] );
 		if ( 'edit' === $context ) {
 			$this->assertEquals( $tax_obj->cap, $data['capabilities'] );
 			$this->assertEquals( $tax_obj->labels, $data['labels'] );