City boss Manuel Pellegrini said Silva had suffered a recurrence of an ankle injury which had been dogging him in recent weeks but the Spanish midfielder is not scheduled to undergo a full scan at the club until Wednesday.
While the injury is not believed to be serious enough to rule Silva out for the remainder of the season, he is almost certain to be missing from City's trip to in-form Crystal Palace on Sunday.
Any absence could prove costly for Pellegrini's men whose win over the relegation-haunted Baggies pulled them to within six points of Premier League leaders Liverpool with a game in hand.
But such is Silva's influence over the City side - particularly in the continued absence of Yaya Toure - his involvement is widely believed to be crucial to City's slim hopes of overhauling Brendan Rodgers' men.
Defender Pablo Zabaleta, who headed the opening goal on Monday night, told City's official website: "We know how important David Silva is for the team
With him in the starting XI, it's different.
"He is the one who has everything
He simply makes us play better
Hopefully we will see with his ankle that it is not so bad
Fingers crossed David will be back as soon as possible and fit for the next game."
Meanwhile West Bromwich Albion face a similar anxious wait to determine the fate of full-back Liam Ridgewell who limped off in the dying minutes of the match.
Ridgewell suffered a knee injury with Baggies boss Pepe Mel saying early indications were that the player could miss out on the rest of the season's run-in.
Ridgewell's absence would be another setback for Mel who must rouse his squad for Saturday's clash against West Ham at The Hawthorns with his side still sitting just three points above the relegation zone.
Baggies midfielder Graham Dorrans - whose first-half wonder goal counted for nothing as City effectively wrapped up victory before half-time - told his club's official website: "It was nice to get on the score sheet but it is about getting the points on board and we never did that.
"We kept a good shape and we will take some positives from the game into Saturday
Everyone - apart from everyone in our squad - expected us to come here and lose."
Source : PA
Source: PA