At least 28 people were wounded in the strike in addition to the three killed, said Muna al-Omairi, a lawmaker in parliament who represents Diyala. Diyala health directorate spokesman Faris al-Azawi confirmed the casualties.
The driver of the car crashed into the front gate of the police compound but was unable to break through, police said.
The attack happened just a few blocks from a similar blast Wednesday in which a suicide attacker drove a bomb-packed ambulance into the headquarters of an Iraqi guard force that protects government buildings. At least seven people were killed and 67 wounded.
Also Thursday, police and hospital officials in Baghdad said a roadside bomb killed one pilgrim and wounded 10 others as they were walking to Karbala, a holy city where religious rituals are about to peak in an end to a 40-day mourning period for Shiites.
The pair of attacks in Baqouba followed another suicide bombing Tuesday in Saddam Hussein's hometown of Tikrit that killed 65 people in a crowd of police recruits.
Although violence has dropped sharply since the high point of the war three years ago, the country is still plagued by small-scale attacks that have kept the country on edge and raised doubts about the capabilities of the security forces as American troops prepare to withdraw at the end of this year.
All three suicide attacks occurred in areas of the country where Sunni insurgents have been active for years, underscoring the difficulties in restoring normalcy in a country that exploded into violence after the U.S.-led invasion that toppled Saddam's regime in 2003.
Meanwhile, officials in the northern city of Kirkuk backed off threats to cut Baghdad's power supply after an agreement to give residents in the oil-rich region more electricity each day.
Earlier this week, Kirkuk leaders shut down power lines feeding electricity to Iraq's national grid after local residents protested they had as little as there hours of light and heat in their homes daily.
The agreement would give Kirkuk homes as much as 12 hours of power daily -- about the same as Baghdad -- said Rizkar Ali, chairman of the provincial council that oversees Kirkuk. Iraqi Deputy Minister of Electricity Amir Ahmed said the government "wants to provide power to all provinces equally."