ESPN announced the suspension Wednesday.
"Every employee must be accountable to ESPN and those engaged in our editorial operations must also operate within ESPN's journalistic standards," ESPN said in a statement. "Bill Simmons did not meet those obligations in a recent podcast, and as a result we have suspended him for three weeks."
Simmons' podcast was released Tuesday. He said he thought Goodell lied about not knowing what was on a security video that showed former Ravens running back Ray Rice hitting his wife in an elevator.
Simmons is the editor of the sports website "Grantland," which is owned by ESPN. He also appears on ESPN's NBA studio shows.