The blast occurred on Friday in the Kocamustafapasa district of Istanbul. A police official, speaking on condition of anonymity, said the bomb was believed to have contained plastic explosives.
Muammer Guler, Istanbul's governor, said the man killed in the blast was a street vendor who sold sesame-coated pretzels. A child was among the injured, CNN-Turk television reported.
Video footage broadcast on CNN-Turk showed debris scattered across a residential street in Istanbul, covering the sidewalk and parked cars.
Ambulances with flashing lights moved down the street while police carrying submachine guns tried to keep crowds of people from the site.
A bomb disposal expert wearing protective gear checked nearby garbage canisters.
An armed Kurdish group claimed responsibility for Friday's blast, calling the attack retaliation for the killings of Kurds in southeastern Turkey.
The Kurdistan Freedom Falcons, a small armed group, said:"We declare to the public that our people are not without protection. The Kurdish people will not remain defenceless."
The email note to journalists added: "From now on, every attack against our people will be met immediately by even more violent acts. We will start to harm not just property but lives too. With our actions we will turn Turkey into hell. The bomb attack in Kocamustafapasa, carried out by our action team, was just a warning," the group said.
Seven people have been killed in
the southeast in recent days
The Kurdistan Freedom Falcons is a group believed to be linked to the main insurgent Kurdish group, the Kurdistan Workers Party, or PKK.
The Istanbul bomb blast follows three days of some of the worst street violence in overwhelmingly Kurdish southeastern Turkey in a decade.
Seven people were killed during the rioting, including a three-year-old boy killed on Friday. The fighting pitted angry Kurds against Turkish police and paramilitary police.
Earlier on Friday, bomb disposal teams destroyed a remote-controlled bomb containing C-4 plastic explosives in the Aegean port city of Izmir, NTV television reported.
The bomb was hidden inside a flower pot left by the side of a road frequently used by police, NTV said. It was discovered by a woman who took the pot home.