The defender limped off in last week's 1-1 Champions League quarter-final draw with Atletico Madrid, which saw the Foxes exit the competition 2-1 on aggregate.
Boss Craig Shakespeare had hoped it was cramp but he will now be without the centre-back for Wednesday's clash at the Emirates Stadium.
He said: "Unfortunately Wes won't make it. He has just overstretched his hamstring. It hasn't gone into a full blown pull but we have to be mindful. So as a precaution he is out then we will look towards Saturday."
Midfielder Nampalys Mendy is also now sidelined for the rest of the campaign after having an operation to finally resolve his long-term ankle problem.
Mendy, a £13million signing from Nice last summer, has made just nine appearances this season after initially injuring his ankle in the 0-0 home draw with Arsenal in August. He has not played since February.
"Unfortunately Papy Mendy had to have an ankle operation," Shakespeare added.
"So he had that in France, and he will be back with us doing his rehab. He had a floating bone in there that needed looking after. He's out now until the end of the season."
Islam Slimani will also miss the game at the Gunners with a groin injury with Leicester six points clear of the Premier League's bottom three with six games remaining.
"I'm not sure how many points it will take (to avoid relegation) and the weekend proved that. Teams are capable of winning games and putting points on the board," said Shakespeare.
"We have to make sure we look after our own club. You are not sure what's round the corner."
But Shakespeare dismissed any suggestions Arsenal, seventh in the table, are in crisis after their 2-1 FA Cup semi-final win against Manchester City on Sunday.
He added: "Seeing the Arsenal match it didn't look like turmoil to me, there were players fighting and they thoroughly deserved the win in the end, even though it was a close game."
