The Belgian had come on as a second-half substitute for Nicolas Otamendi, his first appearance after an eight-game spell on the sidelines with a similar injury, but lasted only eight minutes.
"Yes, it is a calf. Nobody understands (how it happened)," City boss Manuel Pellegrini said. "He had a good warm-up, he was working during the week with normality.
"It is difficult to understand. The most important thing is to understand why this happens. That is the most important to focus on now."
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Kompany's importance to City is such that even an impressive display was overshadowed by the prospect of him spending more time in the treatment room.
Raheem Sterling gave City the lead with a header from Kevin de Bruyne's cross before Yaya Toure's low drive and another header from Wilfried Bony made it 3-0 before halftime.
The influential De Bruyne added a fourth with a cool finish before Fabio Borini's consolation for a Sunderland side who have conceded more goals (37) than any other top-flight team.
Pellegrini said his team, who suffered a fifth defeat of the season against title rivals Arsenal on Monday, should have scored more goals.
"I don't think the score reflected the difference between the two teams," he said.
"I am happy that the performance was very good, we played attacking football, and I am happy with the individual performances. The only pity was Vincent Kompany's injury."
City face Leicester City, the surprise Christmas leaders, on Monday when they will have a chance to climb above the Foxes, having moved to within three points of them on Saturday.
(Reporting by Martyn Herman, editing by Ed Osmond)
