Goals from Lucas Moura and Adrien Rabiot in the first 20 minutes looked to have put PSG on course for their first win in three Ligue 1 games.
But Bastia mounted a stunning fightback as Ryad Boudebouz and Francois Modesto brought them level at half-time and Julian Palmieri's second-half double stunned the champions.
Laurent Blanc's side are now down in fourth place after Saint-Etienne won 2-1 at Reims to go third and striker Ibrahimovic called for a response to the Parisian club's latest setback.
He said: "I think we did good the first 20 minutes and after something happened that never happened to me before; winning a game 2-0 and losing 4-2 is the first time. Something happened and we have to wake up.
"We have to analyse the game, I think many factors, many small details made the difference."
PSG face a trip to Saint-Etienne for a Coupe de la Ligue clash on Tuesday and host struggling Evian in Ligue 1 next Sunday.
