ISS alleges that O'Neal attended less than 75% of board meetings over the last year. Due to that record, the firm is suggesting that holders oppose his reelection in a shareholder vote scheduled for April 23.
O'Neal, who joined the board a year ago, is the only member of Papa John's board to receive the recommendation from ISS.
Papa John's had said in a proxy filing ahead of the April 23 annual meeting that the NBA legend was unable to attend several board meetings due to business and broadcasting commitments made prior to his appointment as a director.
Papa John's also said those scheduling conflicts are not expected to recur in 2020.
Shaq has a wide-ranging portfolio, including Krispy Kreme Donuts among other investments. During the NBA season, he is also one of the anchors of the NBA's halftime show on Thursday night on TNT.
Shaq signed a three-year endorsement deal with the pizza chain, after its founder and former chairman and chief executive, John Schnatter, stepped down.
Papa John's shares at last check fell 1.2% to just under $50.
The stock has been one of the beneficiaries of the coronavirus pandemic over the past couple of weeks as people stay home and order in. From March 18 through Friday's close, the stock is up 42%.
Papa John's closed 50 of its franchised stores in China back in February because of the coronavirus.