Silva was taken to hospital for checks on his cheekbone and collarbone after being caught in the face by an elbow from Hammers midfielder Cheikhou Kouyate at the Etihad Stadium.
The 29-year-old required around eight minutes of treatment on the field before being carefully lifted onto a stretcher and carried off.
City are not likely to be in a position to fully update on the Spaniard's condition until later in the week but are now hopeful no serious injury has been suffered.
This comes after the player himself also moved to allay fears about his condition on Sunday evening.
Silva tweeted: "Many thanks to all the messages of support, all the tests have gone well and I'm already home
The 3 points is what was important!"
Team-mate Fernando also expressed hope after the game that the damage was not significant.
"On the pitch it looked like a serious injury but inside the dressing room, when we discussed it - I think he is going to be okay," the midfielder said.
The incident, which occurred in the 67th minute of City's 2-0 win, prompted some debate about Kouyate's actions but home boss Manuel Pellegrini gave the player the benefit of the doubt.
He said: "I always think that a player doesn't want to damage another player
The referee was so near and he decided he was unintentional
Nothing more happens."
Opposite number Sam Allardyce leapt to the defence of Kouyate, who cannot face retrospective action anyway because he was booked at the time by referee Anthony Taylor.
Hammers boss Allardyce said: "It was pretty innocuous
I didn't think it was a foul."
Source : PA
Source: PA