Heaslip required a minor procedure on his back and Ireland teammate Kearney had an operation on a knee injury, a little over three weeks before Gatland names his squad for the tour of New Zealand.
Both players, who missed their national side's final Six Nations match against England last weekend, are now likely to be out of action for several weeks.
Leinster head coach Leo Cullen is unsure exactly when they will return, telling the club's official website: "Jamie just had a procedure done on his back. He had disc issues. Obviously they come on quite quickly.
"It rules him out of the next number of weeks. When we get a report we will find out how long that will be. It sounds like they are reasonably standard procedures. Rob had an issue with his knee. It happened early during training in the week of the England game.
"He had a procedure done during the week after seeing a specialist on Tuesday. That's probably four to six weeks. We'll see how he comes through that."
Heaslip and Kearney have been involved in the Lions' last two tours.