Deputy Prime Minister Hajredin Kuqi condemned it as a "direct threat upon the prime minister and his family."
"The fact that someone has tried to hurt the prime minister and his family for whatever reason is not only criminal, it goes beyond any political hatred or impatience," Kuqi told reporters in the capital, Pristina.
Thaci's private security guards spotted one person trying to break into the two-story house in a suburb of Pristina, police said. They exchanged fire with an unknown number of assailants, who did not manage to get into the house.
The attackers escaped but traces of blood were found, police said, leading authorities to believe one was injured.
Kuqi would not comment on who he believed was behind the attack and called upon authorities to conduct a swift investigation.
"We don't want to believe that this is due to political hatred," Kuqi said. "We trust the authorities and they will have their say."
Relations between ethnic Albanian political parties in Kosovo have been marked by tension and rivalry. Thaci heads an uneasy coalition government forged with the party of late pacifist President Ibrahim Rugova, his one-time main rival.
He is also at odds with former rebel commander Ramush Haradinaj, who was recently acquitted by the U.N. tribunal of war crimes charges and has returned to Kosovo to lead his party, now in opposition.
Haradinaj's Alliance for the Future of Kosovo condemned the attack and urged authorities to find the perpetrators.
"Such criminal acts damage the positive image of the state of Kosovo," the party said in a statement.
Thaci, the former political head of Kosovo's ethnic Albanian rebels, the Kosovo Liberation Army, is regarded as the key figure in pushing for Kosovo's independence from Serbia.
Kosovo declared independence from Serbia on Feb. 17, which was fiercely opposed by Serbia and Russia but supported by several Western nations.