Details are still emerging following the incident, on the south coast of Salalah, close to the border with Yemen.
A third Briton, a man, is said to be in hospital after being injured in the crash, which is believed to have happened on Thursday.
Police in the Middle East are investing driver culpability, and whether or not he had a licence.
Oman’s Ministry of Tourism said three Britons were involved in the crash.
In a statement, 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.