Parker mentioned during a Dec. 13 broadcast of the ESPN show "First Take" that Griffin -- who is black -- has a white fiancee and brought up rumors Griffin is a Republican.
"Is he a brother or is he a cornball brother?" Parker said. "He's not real. He's black, he kind of does the thing. But he's not really down with the cause. He's not one of us. He's kinda black, but he's not really like the guy you really want to hang out with because he's off into something else."
Parker subsequently sent out a tweet apologizing to Griffin.
"I regrettably introduced some points that I never should have and I completely understand the strong response to them, including ESPN's reaction," Parker said. "Perhaps most importantly, the attention my words have brought to one of the best and brightest stars in all of sports is an unintended and troubling result."
In a statement Thursday, ESPN said it has suspended Parker for 30 days and said it has determined "that mistakes both in judgment and communication were made" in preparing the Dec. 13 broadcast and re-airing it later.
"As a direct result, clearly inappropriate content was aired and then re-aired without editing. Both were errors on our part," the statement said.
"To address this, we have enhanced the editorial oversight of the show and have taken appropriate disciplinary measures with the personnel responsible for these failures," ESPN said.