Footage from the blast scene released by AP showed shattered windows in the office block and the broad street in front of the headquarters closed off and full of fire trucks, ambulances and police vehicles.
The Shanxi provincial government and police said the blasts struck at about 7:40 am (2340 GMT Tuesday).
Official statements posted online gave no information about the presumed target or perpetrators and an official with the party propaganda office, Zhang Lei, said he had no additional information.
One of the injured was listed as serious and two vehicles were reported damaged.
Taiyuan is the provincial capital of mountainous Shanxi, which lies to the west of Beijing in China's gritty coal belt.
Demand for the fuel has created vast fortunes for mine owners, but many in the province still live in poverty.
The blasts bore the hallmark of a revenge attack by a disgruntled citizen of the type that occasionally takes place around China.
Assailants angered at perceived injustices have blown up public buses, stabbed officials and attacked schools.
However, security forces are also on edge over an attack in Beijing last week in which three people drove through crowds to Tiananmen Gate before setting their vehicle alight.
The attack killed five people, including those inside the vehicle, and two tourists, and has been blamed on extremist separatists from the restive Xinjiang region.
BA/BA