It has been replaced by likenesses of former President George W. Bush and Hillary Clinton.
According to The Star-Ledger, manager Tom Whalen said "it's just to show we're not anti-Democrat or anti-Republican."
The "Walkin Charlie" game requires patrons to throw baseballs at plates held by the rotating caricatures.
A plastic bag was placed over the Obama character's head - which has large ears and teeth - after some people earlier this week said it was disrespectful to use the president's likeness.
Whalen says a Secret Service agent visited the concession Wednesday and told him none of the employees had urged patrons to throw at the Obama likeness.
Whalen says the Obama figure might return in a few weeks.