Mayor Tunc Soyer of Izmir told CNN Turk that approximately 20 buildings had collapsed.
At least 70 people were rescued from the wreckage, Izmir Governor Yavuz Selim Kosger said.
In central Izmir, Turkish media showed the wreckage of a multi-story building, with people climbing it to reach rescuers.
Buket, a local resident of Izmir's Bayrakli, said," We have a number of families living here and we are waiting hopelessly."
"They've said that under the ruins are four dead bodies, but we don't know who they are. The only thing we can do is wait."
"My niece and my aunt have been saved, but the news about other families is still waiting for us."
"God help us, please, and we do not wish to lose hope."
The Turkish media said the earthquake was felt throughout the Aegean and Marmara regions, where Istanbul is located, but the Governor of Istanbul said there were no reports of damage to the city.
Turkey is among the most earthquake-prone countries in the world, crisscrossed by major fault lines.
In August 1999, when a magnitude-7.6 quake struck Izmit, a city south-east of Istanbul, more than 17,000 people were killed. In 2011, more than 500 people were killed in a quake in the eastern city of Van.