A third Brit, a man, is said to be in hospital after being injured in the crash, which is believed to have happened on Thursday.
Details are still emerging following the incident on the south coast city of Salalah, close to the border with Yemen.
Cops in the Middle East are trying to establish if the driver is to blame and whether or not he had a driving licence.
Oman's Ministry of Tourism said: "It is with deep regret that the Ministry of Tourism has learned of the accident that took place near the Haffa market in Salalah, which affected three British citizens and resulted into the death of two ladies, while a gentleman was injured and is in stable condition.
"The ministry would like to express its deepest condolences to the families of the two victims of this tragic and painful accident, and it wishes the injured a speedy recovery and a safe return to his home country.
"The ministry is liaising closely with all relevant authorities in order to provide assistance whenever needed."
A post on social media from the Royal Oman Police said preliminary investigation "indicates that the cause of the accident is the driver's deviation from the track".
The identity of the victims, and how long they have been in Oman for, is not yet known.
Salalah is 541 miles southwest of the Oman capital, Muscat, and it is a popular tourist destination in the region.
The Sultanate of Oman is on the southeastern coast of the Arabian Peninsula, bordering with Yemen, Saudi Arabia, and the United Arab Emirates.
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