Wilshere, who was captaining Arsenal at Stamford Bridge, was substituted in the second half after he was seemingly hurt in the process of blocking a cross.
Arsene Wenger confirmed after the match that Wilshere had suffered a sprain, but the Frenchman was unsure how long the midfielder would be out of action.
Wilshere has suffered from a range of ankle injuries during his career, but he has been enjoying a run of games for Arsenal after recovering from a broken leg sustained on loan at Bournemouth last season.
And the 26-year-old, who has made 11 Premier League appearances this season, assured supporters he will not be out of action for long and could even return against his old club.
"Thanks for all the messages and support after last night," Wilshere posted on Twitter. "Good news is I should be back in a couple of days."
Arsenal drew 0-0 with Chelsea in the first leg of the semi-final, with the return match to be played at the Emirates on January 24.