A police spokesman told Reuters: "The bomb exploded on a bicycle... The injured are being treated at two local hospitals."
The person who died had been receiving treatment at one of the hospitals.
Cahit Kirac, the local governor, appealed for calm, while Aziz Kocaoglu, Izmir's mayor, said he did not think there was any connection between the attack and the planned demonstration.
The blast shattered the windows of several houses and windshields of cars.
Police are searching for a suspect who had allegedly left the bicycle at the scene.
Witnesses reported seeing a blue nylon bag on the bicycle.
A range of fighter groups operate in Turkey, including Kurdish separatists, radical Islamists and far-left activists.
Kurdish groups have in the past carried out small attacks in the Izmir area, which is home to a large Kurdish population.