The Oneida Indian Nation said the first advert will run on radio stations in Washington before the team hosts the Philadelphia Eagles in its NFL season opener on Monday night.
In the advert, Oneida Nation leader Ray Halbritter says NFL Commissioner Roger Goodell should "stand up to bigotry" by denouncing "the racial slur" in the team's name.
"We do not deserve to be called redskins," the Oneida leader says in the advert. "We deserve to be treated as what we are - Americans."
The advert acknowledges Mr Goodell had rightly been critical this summer after an Eagles wide receiver was caught on video making a racial slur against African-Americans.
The adverts will be launched as the Washington Redskins face a fresh barrage of criticism over their name, with local leaders and pundits calling for a name change.