Interior Ministry spokesman Brig. Gen. Saad Maan confirmed the toll from the attack, which took place in the mainly Shiite al-Bayaa neighborhood.
The Islamic State group claimed the bombing in an online statement circulated by its Aamaq news agency. The Sunni extremist group said it was targeting Shiites.
The extremist group has carried out near-daily attacks in Baghdad despite suffering military setbacks elsewhere in the country, including in the northern city of Mosul, where US-backed Iraqi forces have been waging a major operation since October.
The US State Department condemned the attack at the car dealership, saying such attacks show the extremist group's "utter contempt for human life and its efforts to sow discord and division among the Iraqi people."
Another four attacks in and around Baghdad killed eight people and wounded around 30, police and medical officials said. They spoke on condition of anonymity because they were not authorised to brief reporters.