Four more have been reported dead in Iraq. The death toll is likely to rise.
The earthquake sparked panic, with residents fleeing their homes for the streets.
Mosques in the Iraqi capital Baghdad have been saying prayers through loudspeakers.
Many of the victims were in the town of Sarpol-e Zahab, about 15km (10 miles) from the border, Iran's emergency services chief, Pir Hossein Koolivand, said, according to Iranian state television channel IRINN.
Damage was reported in at least eight villages, the head of Iran's Red Crescent Organisation, Morteza Salim, told the channel.
"Some other villages have suffered power cuts and their telecommunications system has also been disturbed," he said.
Rescue teams were being hampered by landslides, Mr Koolivand said.
The quake hit 19 miles (30km) southwest of Halabja, near the northeastern border with Iran, the US Geological Survey (USGS) said.
The occurred at a depth of 33.9 km (21 miles), and tremors were felt in Turkey, Israel and Kuwait.