The former Arsenal midfielder, who joined West Ham on a three-year deal this past summer after being released by the Gunners, is ruled out for six weeks.
Wilshere, 25, underwent 'minor' ankle surgery earlier this week, having been plagued by similar injuries down the years.
But although Pellegrini admits that Wilshere is 'very upset, the Chilean manager hopes that the England international can recover quicker on the basis that he has been here before.
"He was working so well that of course he was very upset about what happened," he told Football London.
"He is a player, who maybe is not too old, but he has a lot of experience with injury so I hope he will know about what is the best way to recover as soon as he can.
"I spoke with him before he started the week. He felt the pain in his ankle and we hope he will recover as soon as he can."
In Wilshere's absence, West Ham put a four-game losing streak behind them to beat Everton at Goodison Park on Sunday.
It's a morale-boosting first win for the Irons, and they need the lift in spirits because a visit of Chelsea awaits on Sunday afternoon.
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