A child swept away by flash flooding was among four deaths on Sunday, also including two Asian men who died when a building was hit by a landslip.
Tropical Cyclone Shaheen was downgraded to a tropical storm and then a tropical depression after making landfall north of the capital Muscat late on Sunday.
On Monday, Oman's air force used helicopters to winch stranded survivors to safety on the country's northern coast. A prisoner was rescued from a rooftop in Suwayq, police said.
Trees were felled and streets were flooded in many areas but Muscat was mainly back to normal and the civil aviation authority said the "direct effects" of Shaheen were over.
"During previous cyclones, the sultanate was not affected. Cyclone Shaheen had a direct impact, especially on Al-Batinah area," Muscat resident Mohammad al-Alawi told AFP.
Across the Gulf in Iran, six people were reported dead on Sunday while the United Arab Emirates, which borders Oman, was also put on alert.