The Republic take on Slovakia in the play-off in Bratislava on March 26.
The winner will face Northern Ireland or Bosnia and Herzegovina in the play-off final.
McClean has been a key player for the Republic in recent years and his absence would be a major blow for boss Mick McCarthy.
The 30-year-old was substituted during the home defeat which sees Stoke remain 21st in the Championship.
“Stoke City can confirm that James McClean is facing several weeks on the sidelines and that Thibaud Verlinden will miss the remainder of the campaign after they both sustained injuries in last night’s defeat by Preston,” the club said.
“James has a medial ligament knee injury, whilst Verlinden – who had to be withdrawn from the action just five minutes after joining the action as a substitute – has an ACL knee ligament injury.
“We wish both players a speedy recovery.”