The influential playmaker succumbed to an ankle problem that has been plaguing him for a few weeks in the 70th minute of City's crucial victory over the Baggies which came courtesy of goals from Pablo Zabaleta, Sergio Aguero and Martin Demichelis.
City boss Manuel Pellegrini was unsure of the extent of Silva's injury when quizzed in the after match but did have some good news by stating that Yaya Toure, who has missed the past two games with a leg problem, will be fit for Sunday's trip to Crystal Palace.
"David Silva has a problem with his ankle, we will see tomorrow - he has played the last three games with pain but tomorrow we will have news," Pellegrini told Sky Sports.
"He played all the last games with the pain, and it has now increased - so it is very difficult for us to say [how bad it is], the doctor will know."
He added: "Yaya I think can be fit for next game."
City now sits six points behind league leaders Liverpool with one game in hand meaning they have to win their remaining four fixtures and hope the Reds cop at least one defeat in their final three outings to clinch the 2014 title.
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