The French defender, called up by his country for the first time earlier this week, was stretchered off after 37 minutes after suffering what initially appeared to be a knee injury.
He was replaced by Fernandinho and will be assessed over the next 24 to 48 hours.
“I think he’s gone to hospital,” revealed Pep.
“It doesn’t look good. I don’t know right now what he has done, but we will know tomorrow.
“We’ll see. They’re diagnosing what he has right now. I’m waiting for the doctor to call me. He might be out for a while.”
Asked whether Fernandinho will be a natural replacement if Laporte is side-lined for any period of time, the City boss added: “I don’t know. He’s a holding midfielder and everyone knows that. Me included.
“But i think he has the qualities to play at centre-back. He’s intelligent, he’s fast, he’s strong and he can head the ball.
“He can see what’s happening in front of him. He can play in both positions.”