The shallow quake hit near the city of Javanrud, some 460 kilometers (285 miles) west of the capital Tehran. But the majority of the casualties were in the town of Tazehabad, northeast of Kermanshah.
The head of the emergency department at Kermanshah University of Medical Sciences, Saeb Sharidari, said the three dead were a pregnant woman, her eight-month fetus and a 70-year-old man who suffered a heart attack.
Local officials said that electricity had been cut from 70 villages but that it was restored to at least 50 villages by dawn.
There have been more than 65 aftershocks.
Kermanshah Governor Houshang Bazvand said at least 500 buildings had been destroyed and would need to be completely rebuilt.
There were potential problems with drinking water due to damaged infrastructure in villages, but the local Red Crescent chief, Mohammad Reza Amirian, said it had not yet been necessary to distribute food and tents.
Authorities said rescue teams had been deployed to the area. Interior Minister Abdolreza Rahmani Fazli planned to travel there Monday. President Hassan Rouhani ordered him to provide immediate relief to the earthquake-stricken region.
The tremor also triggered six rockslides, blocking roads in the region.
A crisis center was set up, with hospitals and relief organizations placed on alert.
But the local director of crisis management, Reza Mahmoudian, said that the situation was under control and no request for help had been sent to neighboring provinces.
The quake was felt as far away as Baghdad, according to Iraqi state television, which also said there were no injuries recorded.
National television aired images of bricks and masonry that smashed a sedan, shattered glass filling a stairwell and cracks in walls. It said every city in Kermanshah Province felt the initial temblor.
Images on social media showed people being rushed to hospitals, but suggested relatively light damage to infrastructure.
Iran sits on top of two major tectonic plates and sees frequent seismic activity.
Kermanshah is still recovering from a devastating 7.3-magnitude quake that struck last November, killing 620 people in the province and another eight people in Iraq.
That quake left more than 12,000 people injured and damaged some 30,000 houses, leaving huge numbers homeless at the start of the cold season in the mountainous region.
Local officials said the estimated cost of reconstruction would be measured in the billions of dollars. There was criticism that much of the new social housing built as part of a scheme championed by ex-president Mahmoud Ahmadinejad had failed to withstand the tremor.
Iran’s deadliest quake in recent years was a 6.6-magnitude tremor that struck the southeast in 2003, decimating the ancient mud-brick city of Bam and killing at least 31,000 people.
In 1990, a 7.4-magnitude quake in northern Iran killed 40,000 people, injured 300,000 and left half a million homeless, reducing dozens of towns and nearly 2,000 villages to rubble.
AFP, AP and Reuters contributed to this story.