Index: src/wp-admin/includes/plugin.php
===================================================================
--- src/wp-admin/includes/plugin.php	(revision 44656)
+++ src/wp-admin/includes/plugin.php	(working copy)
@@ -1048,6 +1048,11 @@
 			foreach ( $translations as $translation => $data ) {
 				$wp_filesystem->delete( WP_LANG_DIR . '/plugins/' . $plugin_slug . '-' . $translation . '.po' );
 				$wp_filesystem->delete( WP_LANG_DIR . '/plugins/' . $plugin_slug . '-' . $translation . '.mo' );
+
+				$json_translation_files = glob( WP_LANG_DIR . '/plugins/' . $plugin_slug . '-' . $translation . '-*.json' );
+				if ( $json_translation_files ) {
+					array_map( array( $wp_filesystem, 'delete' ), $json_translation_files );
+				}
 			}
 		}
 	}
Index: src/wp-admin/includes/theme.php
===================================================================
--- src/wp-admin/includes/theme.php	(revision 44656)
+++ src/wp-admin/includes/theme.php	(working copy)
@@ -88,6 +88,11 @@
 		foreach ( $translations as $translation => $data ) {
 			$wp_filesystem->delete( WP_LANG_DIR . '/themes/' . $stylesheet . '-' . $translation . '.po' );
 			$wp_filesystem->delete( WP_LANG_DIR . '/themes/' . $stylesheet . '-' . $translation . '.mo' );
+
+			$json_translation_files = glob( WP_LANG_DIR . '/themes/' . $stylesheet . '-' . $translation . '-*.json' );
+			if ( $json_translation_files ) {
+				array_map( array( $wp_filesystem, 'delete' ), $json_translation_files );
+			}
 		}
 	}