The suicide bomber died and three embassy employees, all Kyrgyz nationals, were injured, Deputy PM Zhenish Razakov said.
China’s foreign ministry condemned the bombing as an “extreme and violent attack”.
No one has yet said they were behind the suicide bombing.
Chinese foreign ministry spokeswoman Hua Chunying said: “China is appalled and strongly condemns the violent act.”
She said China had “demanded that Kyrgyz authorities take all necessary measures to ensure the safety of Chinese institutions and personnel in Kyrgyzstan, launch a thorough investigation to find out the truth of the incident and harshly punish the perpetrators”.
The vehicle reportedly smashed through the gates and exploded in the centre of the compound, close to the ambassador’s residence.
Social media footage showed smoke billowing above the building.
“As a result of the explosion, only the suicide bomber terrorist died,” Mr Razakov told journalists.
The three injured people were reportedly two 17-year-old embassy gardeners and an unidentified woman.
The chief of security at the Chinese embassy told the local AKIpress news agency that no Chinese were hurt.
As well as Chinese embassy employees, staff at the American embassy nearby were evacuated.
Kyrgyz security officials are at the scene conducting an investigation into the blast, which came a day before the nation marks its independence day.
Kyrgyz authorities conducted several anti-terrorism operations in Bishkek in 2015.
Officials say that some 500 Kyrgyz nationals are believed to have joined so-called Islamic State in Syria and Iraq.