Police Major Abdel-Hussein Minsef said two bombers entered the restaurant and detonated bombs strapped to their bodies, leaving seven police officers and 26 civilians dead, and 19 others injured.
The restaurant, located near the Sheraton and Palestine hotels in central Baghdad, was immediately cordoned off after the attack, which took place at around 9.40am local time.
The restaurant was known to serve breakfast to police and security officials.
Witnesses said the explosion could be heard several miles away.
Samiya Mohammed, a housewife who lives nearby, said she rushed outside when she heard the explosion.
"I went out to see the restaurant heavily damaged. There was bodies, mostly civilians, and blood everywhere inside the place.
"I do not understand why most of the time it is the Iraqis who are killed," she added.
It comes a day after at least six people were killed and 25 others hurt in two car bomb blasts in a mainly Shi'ite district in north-eastern Baghdad.