City enjoyed a great start to the Premier League season under new boss Manuel Pellegrini, romping to a 4-0 victory over the Magpies at the Etihad Stadium.
However, there was one worrying moment for City fans when Kompany had to be taken off after 71 minutes and he will need to be assessed.
But the 27-year-old tweeted later on: "Team was great, I felt great.
"Injury is a blow after all the hard work. I'll be back to that level in no time. Thanks for all the support!"
City are a little short of defenders at present because Matija Nastasic has an ankle problem, although he may return to full training this week.
Micah Richards also sat out Monday's match and so midfielder Javi Garcia came on to line up alongside Joleon Lescott for the closing stages of the match.
City's only other centre-back option is Dedryck Boyata, who did not feature much under previous manager Roberto Mancini.
Pellegrini admitted after the match that he would have to monitor Kompany's progress carefully, saying: "We'll see during the week with Vincent Kompany exactly what he has.
"We will see what the best thing is that we must do."
Pellegrini was pleased with how Man City maintained their level of performance in beating Newcastle.
"For me, the most important thing was the way my team played for the 90 minutes," Pellegrini told Sky Sports. "We didn't play one way when we were winning 2-0, we tried to play football during 90 minutes.
"We were attacking, defending, an aggressive team with possession of the ball, and we scored four goals but I think we had at least six or seven other chances.
"We didn't concede any goals either and for me it's very important the way my team played the 90 minutes."