The Belgian limped off after just seven minutes of the 1-0 last-16 first-leg loss at the Jose Alvalade Stadium and will definitely miss the Premier League leaders' trip to Swansea on Sunday.
Joleon Lescott, who replaced him, also felt pain in his groin during the game but manager Roberto Mancini does not believe that problem is serious.
Mancini said: "I hope that for Vinnie, the injury will be short.
"When you have a calf (injury), it can be a big problem. I hope he can recover in 10 days, two weeks maximum. We will see how it is in another one or two days."
On the positive side right-back Micah Richards, again left out to rest a minor knock, should be fit as City look to protect their two-point lead at the top of the table at the Liberty Stadium.
Mancini said: "I didn't take a risk with Micah because Pablo Zabaleta is injured. Micah will play on Sunday."
City are now staying in Lisbon to train in warm weather for the next two days before travelling directly to south Wales.
City will now have to overcome a deficit to reach the Europa League quarter-finals after Brazilian defender Xandao scored the only goal after 51 minutes.
Sporting controlled large spells of the game and had opportunities to make victory more emphatic, forcing Joe Hart into two particularly good saves.
City, who went close through Aleksandar Kolarov and Gareth Barry, were below par but still have hope of turning the tie around at the Etihad Stadium next week.
Mancini said: "It wasn't a surprise because anything can happen in football, but I don't think we deserve to lose.
"We didn't play very well but could've scored, then conceded a goal, so that is it. We have another 90 minutes and I think it will be a different game. We still have a big chance. Hopefully we will have a chance to score and I think we will score.
"I don't think they had a lot of chances to score. Sporting had players behind the ball always, to play on the counter-attack.
"They had players behind the ball for this reason and I think we had more chances than them."
Mancini did not believe the result would have a negative impact on morale ahead of Sunday's match.
He said: "I am not worried. We will go through in the Europa League and Sunday will be a different game."
Sporting coach Ricardo Sa Pinto warned City before the match they would pay the penalty if they under-estimated their opposition.
Mancini dismissed suggestions he had not paid Sporting enough respect.
He said: "I don't agree with this. I think that every game is difficult and different. We try to play good football. Sometimes we win, sometimes we lose.
"Football is strange, but we have another game and a chance to win the next game."
Mancini hailed Hart's performance and refused to blame him for the goal.
Hart pushed away a Matias Fernandez free-kick and reacted quickly to save from Xandao before being beaten by the Brazilian's second attempt, a nifty backheel.
Mancini said: "Joe is a fantastic keeper and this is his job, I hope he can continue to do this."
Sa Pinto, whose side are fourth in the Portuguese league, felt his side deserved their success and now expects them to complete the job in the second leg.
He said: "I have a lot of respect for Mr Mancini, as a player and a coach, but I have a different opinion.
"I believe Sporting played the perfect game tonight [Thursday]. We did nothing by accident, everything went according to plan.
"It was the maximum performance from my players.
"We knew we had to be perfect to overcome Manchester City, we were playing against the team that are first in the Premier League.
"But we also have a good squad and I do believe we can progress to the next stage of this competition, although it will be a difficult game in Manchester."