Tremors were felt across the Gulf region, across Pakistan and well into north-west India at around 10.45 GMT on Tuesday.
The US Geological Survey said it had measured the earthquake at magnitude 7.8 and gave its location as 50 miles east-south-east of the town of Khash, in Iran.
Though the area is largely desert and mountains, there are several major cities, including Zahedan, only 125 miles away, which has more than half a million inhabitants.
An Iranian official quoted by Reuters said hundreds of dead were expected as a result of the quake. "It was the biggest earthquake in Iran in 40 years and we are expecting hundreds of dead," said the official, who spoke on condition of anonymity.
The 7.8 figure means an extremely powerful quake, on a level with that in Sichuan province, China, in 2008 that killed an estimated 68,000 people.
People in the city of Zahedan poured into the streets when the earthquake struck, Iran's Fars news agency reported.
All communications in the area have been cut, the Iranian Red Crescent's Mahmoud Mozaffar told state television, and rescue teams have been dispatched to the affected area.
"In the aftermath of this earthquake five evaluation teams from the Khash and Saravan branches were sent to the area to assess damage," Mozaffar said.
There has been no serious damage in the Iranian city of Saravan, the Fars news agency said.
In Delhi, more than 1,500 miles from the suspected epicentre in Iran, office workers evacuated buildings as fittings shook and windows rattled. Tremors lasted for around 30 seconds.
"It was very frightening. Everything started moving. I ran into the street," said Rajiv Khanna, an office worker in the south of the Indian capital.
There were reports of tremors felt in Qatar, Bahrain and Abu Dhabi in the Gulf, in Multan in Pakistan and elsewhere.
In 2003, a major earthquake near the Iranian city of Bam, not far from Tuesday's epicentre, killed 30,000.
Iran's Bushehr nuclear power plant was not damaged by the earthquake, an official at the Russian company that built the plant said. The official at Atomstroyexport said he had spoken to a colleague at the plant after the quake and that no damage was reported.
Bushehr, Iran's sole nuclear power plant, is near the Gulf coast in western Iran, while the quake struck in eastern Iran near the border with Pakistan.