“The N.F.L. has hurt us by not resolving the current debacle to the players’ and owners’ satisfaction,” Mr. Schnatter, 56, said on Nov. 1 during a conference call with investors. “N.F.L. leadership has hurt Papa John’s shareholders.”

In an interview on Thursday evening, a spokesman for Papa John’s did not directly answer whether Mr. Schnatter’s comments about the N.F.L. played a role in his decision to step down. But the spokesman, Peter Collins, said that it was the right time for Steve Ritchie, 43, the company’s president and chief operating officer, to become the next chief executive. Mr. Schnatter will remain as chairman of the company’s board.

Pizza is big business during football games, but the TV viewership has dropped from last season. President Trump has blamed the lower ratings on the anthem protests, and Mr. Schnatter said during the conference call that Roger Goodell, the league commissioner, should have handled the situation faster.

“Leadership starts at the top, and this is an example of poor leadership,” Mr. Schnattner said.

His comments about the N.F.L. protests won the praise of white supremacists, and Papa John’s responded by saying it did not want white supremacists or their groups buying its pizzas.

Under Mr. Schnatter, Papa John’s became one of the top pizza chains in the United States, but its stock price has tumbled in the past year, falling by nearly one-third to $59.23 per share, as of Thursday.