The network announced the suspension Thursday, a day after Parker apologized for comments he made during a Dec. 13 episode of "First Take".
Posting to Twitter, Parker said, "I blew it and I'm sincerely sorry. I completely understand how the issue of race in sports is a sensitive one and needs to be handled with great care."
Parker, who is black, was discussing Griffin's role as an African-American quarterback when he noted that Griffin has a white fiance and is rumoured to be a Republican.
Among his comments, Parker said, "Is he a brother or a cornball brother?"