A Kurdish separatist group, the TAK, said it carried out the attack in response to recent violence in the mainly Kurdish south-east of Turkey.
The EU and UN have expressed concern over rising tensions.
The bomb went off in a rubbish bin in the Kocamustafapasa district of Istanbul, officials said.
| We will turn Turkey into hell Kurdish militant group TAK |
It killed a food vendor whose stall had been set up nearby, Istanbul Governor Muammer Gulerbus was quoted as saying by the AFP news agency.
Mr Gulerbus added that two of the injured were in a critical condition.
Several hours later, the TAK (Kurdistan Freedom Falcons) said the attack was carried out by the group's "reprisal units".
"From now on, every attack against our people will be met immediately by even more violent acts, " TAK said in an e-mail sent out to news agencies.
"We will start to harm not just property but lives too. With our actions we will turn Turkey into hell," it said.
Rising tensions
The protests in the south-east began after funerals of 14 suspected Kurdish rebels killed by the military last weekend.
Seven people were killed in clashes between Kurds and the Turkish riot police in and around the regional capital, Diyarbakir.
The EU urged the Turkish government on Friday to improve the cultural rights of Kurds and to develop the region's economy.
A UN human rights envoy, Martin Scheinin, praised the reforms introduced by Ankara over recent years but said that more needed to be done to reduce tensions over socio-economic problems, including unemployment and access to education.
Relative calm has since returned to Diyarbakir.