The midfielder, captain for the night, went off in the second half of Wednesday's Carabao Cup semi-final first leg against Chelsea.
He suffered an ankle sprain when making a block, and the setback made him a doubt for Sunday's Premier League match with Bournemouth, where he spent last season on loan.
But Wilshere believes he will soon be back in action.
He wrote on Twitter on Thursday evening: "Thanks for all the messages and support after last night. Good news is i should be back in a couple of days"
It remains to be seen whether Wilshere is considered for the Bournemouth game but there seems little danger of him being sidelined by the time Crystal Palace visit the Emirates Stadium on January 20.