The influential defender took a knock in City's Champions League loss to CSKA Moscow on November 5 and then missed the 2-2 draw at QPR in the Barclays Premier League three days later.
Manager Manuel Pellegrini expressed hope the problem was not serious but Kompany did also pull out of Belgium's Euro 2016 qualifier against Wales last week.
City published a picture of Kompany back in training online at cityblog.mcfc.co.uk on Thursday.
Kompany's return raises the possibility that he could feature against Swansea at the Etihad Stadium on Saturday, although Pellegrini might prefer to hold him back to face Bayern Munich next Tuesday.
City's home clash with the German giants is a vital one, with the Premier League winners needing a positive result to maintain interest in the Champions League.
In four games in the competition so far, City have claimed just two points and they have little room for error heading into their penultimate Group E fixture.
City are also hoping playmaker David Silva can recover from a knee injury in time for the Bayern match.
The Spaniard has been sidelined since suffering the setback in last month's Capital One Cup loss to Newcastle but returned to light training last weekend.
Striker Edin Dzeko and left-back Aleksandar Kolarov are both expected to be out until next month with calf injuries.
Source : PA
Source: PA