The Spaniard was stretchered off just after the half-hour mark having twisted his ankle attempting to make a low clearing header and he was later spotted leaving the Liberty Stadium on crutches.
A fracture has been ruled out and Flores will travel to Dubai for next week's warm-weather training camp.
But Laudrup admits an injury to one of his key players is an unwelcome headache, just two weeks before the Welsh club's first major cup final.
He said: "We have to wait to see if it is only a twisted ankle or it could be more damage with the ligaments.
"We have to wait for the scan but if it is ligaments he would definitely be out of the final.
"We will see first if there is anything that needs surgery, the more things we can exclude right now the better.
"If it is ligament damage we need to see how bad it is and make a decision from there."
Flores' injury was the only negative as Swansea hammered QPR for the second time this season, having triumphed 5-0 at Loftus Road on the opening day of the season.
Early strikes from Michu and Angel Rangel set the hosts on their way at the Liberty Stadium. Substitute Bobby Zamora pulled a goal back for the R's, only for Pablo Hernandez to restore Swansea's advantage with an excellent finish before Michu added his 18th of the season.