The former Chelsea boss was out shopping with his family when a fan with a mobile phone repeatedly asked for a photograph with him.
Police were called to a shopping centre near Madrid on Thursday evening after the fan claimed he had been assaulted.
Mourinho, who was with two bodyguards, denies any wrongdoing.
A probe was underway last night after shopping centre security guards intervened and called police at the request of the man claiming to have been assaulted.
A spokesman for the Civil Guard in Madrid, the police force investigating the incident, said: "I can confirm that officers at our station in Majadahonda have received a formal complaint from a person who claims he was the victim of an assault by Jose Mourinho.
"We are investigating his claim. At this stage we cannot comment on whether there is any truth to the claim or not."
A Real Madrid spokesman declined to comment.