“Every employee must be accountable to ESPN and those engaged in our editorial operations must also operate within ESPN’s journalistic standards,” the company said in a statement. “We have worked hard to ensure that our recent N.F.L. coverage has met that criteria.”

Image ESPN suspended Bill Simmons for three weeks. Credit... Amy Sussman/Getty Images The New Yorker

Simmons, ESPN said, “did not meet those obligations.”

On his Grantland podcast, Simmons said: “Goodell, if he didn’t know what was on that tape, he’s a liar. I’m just saying it. He is lying. I think that dude is lying. If you put him up on a lie-detector test, that guy would fail.” He added: “I really hope somebody calls me or emails me and says I’m in trouble for anything I say about Roger Goodell, because if one person says that to me, I’m going public. You leave me alone.”

ESPN has removed the podcast from the Grantland website.

This is the third suspension for Simmons in his career at ESPN, and the most serious. In 2009 and 2013, he was barred from using Twitter for messages that violated company guidelines. In the latter case, he said that a quarrel on ESPN2’s “First Take” between Skip Bayless and the Seattle Seahawks was “awful and embarrassing.”

Simmons was unavailable for comment on the latest ESPN action against him.

Simmons’s latest suspension is not the first one at ESPN connected to the Rice case.

In July, Stephen A. Smith, a commentator on “First Take,” was discussing Rice and the two-game suspension that Goodell initially imposed. In rambling remarks, Smith suggested that women should avoid provoking men into assaulting them. He was soon after suspended from a week from “First Take” and his ESPN Radio show.