Brazilian Silva, who has made 23 league appearances this season, left the field in the second half after sustaining the injury during an attempt to block Jean-Philippe Mateta's shot.
"Yes, minor injury... he (Silva) is out for tomorrow. He's not available. Afterwards, we need to assess him," Pochettino told reporters on Friday.
Midfielder Carney Chukwuemeka will also miss the game with a twisted knee but Spanish goalkeeper Robert Sanchez, out since December with a knee injury, is available, the manager added.
Chelsea held City to an eventful 4-4 draw at home in November when Pochettino was booked for a post-match outburst aimed at referee Anthony Taylor.
"It is not going to happen again. I was so upset with the referee and I went like an arrow onto the pitch for the referee. It was a big mistake ... I feel really bad so I apologise again," Pochettino said of the incident.
He added that facing City would require Chelsea to attack.
"You need to be brave, to force them to defend, to run backwards, face to the goal," he said.
"It's a team that can dominate you and it's going to make (you) suffer. I think the most important thing that we realised is we need to attack."
Saturday will see Chelsea's England midfielder Cole Palmer return to City, where he spent 13 years before leaving in the close season.
"He is very grateful for Man City and he left the club as he wanted to find another challenge," Pochettino said of the 21-year-old.
"Man City are doing really well and are one of the best teams in the world, it is not easy to find a space for a young guy," he added.
Chelsea, 10th with 34 points, are 18 points adrift of City, who are chasing their fourth title in a row as they trail leaders Liverpool by two points, albeit with a game in hand.
