The Juventus man fears that he may not be fit to play against the Bavarians in Tuesday's Champions League quarter-final first leg after Esteban Cambiasso's late lunge
The Bianconeri ran out 2-1 winners at San Siro but some gloss was taken off the victory when Giovinco was caught by bad tackle from Esteban Cambiasso deep into stoppage time, an incident which earned the Argentine a straight red card.
The 26-year-old limped off the field after the game and confirmed to Tuttosport that he is a doubt for the quarter-final first leg in Germany.
"My ankle hurts and we are a little worried," said the forward.
The Derby d'Italia defeat leaves Inter in seventh in Serie A and the frustration in Cambiasso's lunge was evident, though the Nerazzurri midfielder was quick to repent.
"Yes, I apologized to him [Giovinco] and I think that is the most important thing," the 32-year-old said.
"I am sure that Sebastian understood. Anyone who has played football knows that if you wanted to hurt someone, you wouldn't go in as low as that. I arrived a split-second late."
Andrea Stramaccioni was also quick to leap to his player's defence, suggesting that his character was not in any way malicious.
"I have already told everyone that Esteban is a good man and a true professional," the Inter boss added.
"No one needs to lecture him about this."