According to local government officials, the incident took place in Gardez city on late Sunday afternoon.
The officials further added that a vehicle of the Afghan national army was targeted in the first blast, while the second blast targeted a vehicle of the Afghan national police forces.
Deputy police chief, Mohammad Zaman said at least two policemen and three civilians were injured in the second blast.
The third blast did not incur any casualties but four civilians were injured following two other explosions near the civilian hospital in Gardez city, the officials said.
No group including the Taliban militants has so far claimed responsibility behind the explosions.
Paktia is among the relatively volatile provinces in eastern Afghanistan where anti-government armed militant groups including the Taliban militants and Haqqani Network insurgents are actively operating in a number of its districts.