Can we discipline employee who posted rude photo on Facebook?

Q. An employee complained to management that she saw an offensive Facebook post by one of her co-workers. The post was about another employee. The post was a picture of a monkey and the caption read "my co-worker." Next to it was a picture of the co-worker in her company uniform and the caption read, "Now here she is without hair." Being that he posted a picture of her in a shirt with our company logo on it, is there anything we can do to discipline him? Can we at least question him and ask him to remove it since she is in uniform? – Stacey, New York