Cairney has picked up a foot injury, which he suffered in the Premier League game against Burnley at the weekend.
He came off in the 78th minute in that game. Now he will be on the sidelines for two to four weeks, depending on how quickly he recovers.
The midfielder also pulled out of the Scotland squad for the upcoming internationals.
"Tom Cairney is going to be unavailable for the Brighton game," Jokanovic said to Sky Sports.
"He has a foot injury and we still need to assess him but it is our expectation that he will be unavailable for a few weeks.
"We must assess him, he is going to be out for a few weeks.
"Yes, this is a big loss for us."