The blast took place in the early
hours of Tuesday
The bomb shook the three-storey café in the city’s main commercial district Kizilay, killing the woman and injuring at least one other person.
Officials are investigating if the blast was a suicide bomb attack.
"It is believed she was a member of DHKP-C (Revolutionary People's Liberation Party-Front)," said a police authority.
Witnesses said a young woman was seen entering a washroom where the blast is believed to have occurred.
Only a few customers were in the café, frequented by students, at the time.
No one claimed responsibility for the blast. Turkish police officials said they were exploring whether the blast was a suicide attack, but had not ruled out the possibility the bomb was accidentally detonated.
Police closed off the area and were sifting through the debris of the charred building. Medical investigators identified the victim as a woman aged between 30 and 35 years old.
Café owner Sadullah Kayalar told reporters he had received no warnings ahead of the attack.