The interior ministry said 25 people were killed, including at least 10 policemen, and 32 were wounded in the blast on Thursday.
The ministry said the bomber had stopped his car at the first checkpoint and was having his vehicle checked for explosives when he detonated the bomb.
Earlier, a police official said the car bomber had driven at high speed into the checkpoint.
Assailants also set off roadside bombs aimed at police patrols across the capital, killing at least four people and wounding a dozen others, police said.
The roadside blast in the Azamiyah area of Baghdad killed two policemen and two bystanders, according to a police spokesman.
At least seven others, two policemen and five civilians, were wounded, he said.
Another bomb in the capital wounded four civilians but no police in Karradah, which is mostly Shia but has a large Sunni minority.
In Iskandariya, 50km south of Baghdad, a roadside bomb killed one policemen and wounded two pedestrians, police said.