Jade Jagger, 36, informed police on Thursday that she had gone straight to her luxury Arbat Park Hyatt hotel in the centre of the Russian capital after flying into Moscow's Domodedovo airport.
"The foreigner discovered the loss of her passport in her hotel and informed police immediately," the source said. "A form was filled out in line with the correct procedure. If the document is found, or anyone hands it in, the police will tell the hotel where Jade Jagger is staying straight away."
The British Embassy declined to comment.
Under Russian law, everyone, both Russians and foreigners, must be able to produce a passport at any time. Russians are issued with internal passports for domestic use.
Jade Sheena Jezebel Jagger is a jewelry designer, and an ex-model. She is the daughter of Mick and Bianca Jagger.