The Omani news agency ONA said at least 32 people had been killed and 30 were missing.
Three people were reported killed in Iran on Thursday and nine were missing.
ONA said winds from Gonu, now downgraded to a Category One hurricane, were moderate and sea waves were about two metres high.
State media said roads and houses in Iran's southeastern province of Sistan-Baluchestan had been damaged and many coastal areas were cut off by flooding.
Meanwhile, the United Arab Emirates' port of Fujairah, one of the world's largest ship refuelling centres, reopened on Thursday morning after closing the day before.
Gonu peaked as a maximum-force category five hurricane on Tuesday and faded to a category one hurricane on Wednesday.
Oman has started carrying out tests on pipelines in Mina al Fahal, the country's only terminal for its 650,000 barrels per day crude exports, after a three-day closure due to the Cyclone, according to a shipping source.
He said: "They are carrying out tests for pipelines to see if they are in order, to check if they could start operating again."
Petroleum Development Oman, a major state-owned firm, said on Thursday that operations and facilities had escaped damage.
The storm had raised fears of a disruption to exports from the Middle East, which pumps over a quarter of the world's oil, pushing prices to around $71 a barrel on Thursday.