The Art section of Datahub.io has several good candidates -
For example, the Wikimedia Paintings page. It's not an API, but you can download all image files from this page by a command like this:
wget -r -P /save/location -A jpeg,jpg,bmp,gif,png http://commons.wikimedia.org/wiki/Category:Paintings
(at the moment, this command doesn't work for me, but it should be possible - details)
Another option might be the Victoria and Albert Museum API -
Also consider Freebase (which is being transferred to Wikidata). An example of Monet's paintings is
And the same query can be made via the API.