The quakes struck near the city of Tabriz and the town of Ahar, but most of the casualties are thought to be in outlying villages.
Reports say phone lines to many villages have been cut off, making rescue efforts harder.
The US Geological Service measured the quakes at magnitude 6.4 and 6.3.
“The quake has created huge panic among the people,” said one resident of Tabriz.
“Everyone has rushed to the streets and the sirens of ambulances are everywhere.”
The towns of Haris and Varzaqab in East Azerbaijan province were among those that suffered casualties, Khalil Saei, local crisis committee chief, told state TV, according to the Associated Press.
Officials say at least four villages have been completely destroyed, with another 60 villages suffering damage ranging from 50% to 70%.
The two earthquakes came within minutes of each other, according to seismology experts at Tehran University.
Dozens of rescue workers have been sent to the region, but the onset of darkness has hampered relief efforts.
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