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.
One of the three men who carried out an attack on Istanbul’s Ataturk airport in June was said to be from Kyrgyzstan. The suicide gun and bomb attack, which Turkey blamed on IS jihadists, left 44 people dead and 240 injured.
Chinese have been targeted in Kyrgyzstan in the past, including in 2000 when one official was shot dead in an attack blamed on Uighurs, who form a restive population of China’s western Xinjiang province.
Kyrgyz border guards killed 11 people believed to be members of a Uighur anti-Chinese militant group after they were said to have illegally crossed the border in 2014.
In its travel advice to Kyrgyzatan, the UK government warns of an underlying threat from terrorism.
It says there has been some terrorist activity and armed violence, particularly south and west of the city of Osh.
The radical pan-Islamic group, Hizb ut-Tahrir, is said to have a presence in the country. It was banned in 2006 amid accusations of links to the Taliban and al-Qaeda.