The Belgian was withdrawn at half-time in Sunday’s Manchester derby and will now miss City’s visit to South Wales, but Pep Guardiola is hopeful he will not be without his captain for too long.
“He [Kompany] can’t play at Swansea,” said the Catalan at Tuesday’s pre-match press conference.
“I think it is less than we expected so hopefully he is back in a short time, but I don't know.
"He has a muscular injury.”
The Blues go into the game against Paul Clement’s men on the back of the morale boosting 2-1 victory over Manchester United.
It was a performance to savour and stretched City’s lead at the top of the Premier League table to 11 points and leaves them on the brink of a Premier League record 15 consecutive wins.
The manager, however, is keen to move and focus his players' minds on the impending test at the Liberty Stadium.
“The game was good, we played our way,” explained Guardiola.
"I leave that situation in the past. I am going to focus on the [Swansea] game, focus on what have to do to beat our opponents.
"I said to my players forget about what happened. Swansea is now the most important thing and after that, Tottenham.
"It’s what I have done all my career and is what I am going to do in the future.
"I try to give to my players the best advice I can, because first we represent ourselves and then we represent the Club."
Meanwhile, the boss believes his squad can take pride in how they’ve performed in the Premier League, against the backdrop of Champions League football.
With the previous two champions, Leicester City and Chelsea, having lifted the trophy without the pressure of European football, Pep believes it is a testament to his squad's quality that the Champions League not impacted their domestic form.
"Obviously not playing in the Champions League has an influence, so that speaks a lot of the merit of what we’ve done up to now," he added.
"That does not guarantee that we will win trophies at the end of the season but that doesn’t change my opinion of the way we’ve played so far.
"In the future we can drop points, the league will be open again. People will think we have already won the Premier League, I don’t think that.
"Obviously last season Chelsea played one game a week over the whole season.and won the league.
"Now we have played so many games so we are really happy and proud of what we’ve done so far."