A short YouTube film showed the member of the Commission for the Promotion of Virtue and Prevention of Vice jumped over a car and assaulted the couple.
The film, published in the Arabic language daily 'Ajel', showed a large crowd tried to stop the Commission member as the Briton was heard in the background screaming at him.
Newspapers quoted the Commission’s chairman Abdul Lateef Al Shaikh as saying he had ordered the formation of a committee to probe the incident.
“We will announce the outcome of the investigation soon. If the committee finds that it was the fault of the Commission member, then we will take stringent measures again him.
"We will not accept that any foreigner living in the Kingdom is harmed.”
'Ajel' said the woman also assaulted the Commission member during the scuffle, adding that the Commission is also trying to determine where the incident occurred.
'Ajel' and other newspapers said the man could be British while his wife might be Saudi.