An intruder stole valuables including a Louis Vuitton bag, 11 luxury watches, various items of Cartier jewellery and 10 glasses studded with diamonds and pearls, two police sources told news portal RBC.
Maluma, who is one of the biggest names in Latin music, is in Russia to watch the football World Cup.
Moscow police opened an investigation into suspected theft on Tuesday, both RBC and Interfax said, quoting a source as saying he had been staying at the Four Seasons Hotel near the Kremlin.
A spokeswoman for the hotel gave no details of the incident but told Reuters that an investigation was underway. "We treat the question of security for our guests and their belongings very seriously and immediately informed the police," she said in an email.
Just after midday Moscow time, Maluma wrote on social media that he was travelling to the city of Saransk where Colombia was due to play Japan, posting a picture of himself wearing a Colombian football jersey in front of a plane.
"En route to SARANSK. Today we finally accompany our team COLOMBIA!!" Maluma, who is from the city of Medellin, wrote on social media.
Colombia lost 1-2 in an upset against Japan.