However, no one was hurt by the blasts, according to a Kosovo police officer.
The two other explosions took place in front of the parliament building and the European agency for reconstruction and development in Pristina, as well as a restaurant which is close to the headquarters of the Organisation for Security and Cooperation in Europe (OSCE).
"There were no victims and no injuries and the police and KFOR (the Nato multilateral force) have sealed off the area and begun an inquiry," spokesman Refki Morina said.
He refused to speculate on the identity of the bombers or their motives.
A UN vehicle parked outside the UN mission was destroyed by a fire after the blast and two others were damaged.
A witness at the Zora restaurant said he had "not seen anything suspicous" before the explosion.
Experts are evaluating the damage caused by the blasts, for which nobody has yet claimed responsibility.
Central Pristina was cordoned off to keep passers-by and cars away and local and UN police officers are on patrol.
Kosovo has been under UN administration since June 1999.