It was not clear whether there was any political motive for the shooting of Elvis Pista, who was killed as he left a restaurant in the southern town of Rahovec with his wife and some friends, the police said.
"He was shot from behind with a fire arm, at a distance of five meters," said a police statement emailed to Reuters.
Kosovo authorities have not yet certified the results of last Sunday's election, so it is not known whether Pista had won a seat in parliament with Thaci's ruling Democratic Party of Kosovo (PDK). However, an election commission official said he won most votes in his area for the PDK.
Thaci said the authorities were doing everything they could to track down those responsible for the shooting.
The PDK won most votes in Kosovo's election but three opposition parties have vowed to unite to form a government and thwart Thaci's bid for a third term in office.
Kosovo remains mired in poverty and corruption six years after winning its independence from Serbia with Western backing.