In a tweet on Monday, the US State Department advised all citizens to avoid the area following reports of a shooting near the embassy.
Officials have described the closure as being due to an "ongoing security incident".
The alert came just moments after the Russian envoy, Andrey Karlov, was gunned down at the photo exhibition.
The embassy compound is approximately 2.5 miles away from the art gallery where Karlov was shot and killed.
Moscow said the assault was a "terrorist act."