The thief entered the renovated seven-story luxury house that Ronaldo owns in Madeira’s capital through the garage after it was believed to have been left open by a maintenance worker.
Several items were stolen from the player’s home, including a reported signed Juventus jersey worth €200.
Police are looking at CCTV cameras to identify the burglar.
“The police will not provide other data inherent to the process under investigation, ensuring that appropriate and timely steps are being taken to identify the suspect and the corresponding recovery of the stolen goods,” police authorities told ESPN FC.
Ronaldo started in Portugal’s goalless draw against Spain in Wednesday’s friendly in Lisbon, a game that marked his 200th appearance for his country at both youth and senior level.
The former Real Madrid star spent most of the coronavirus lockdown in his home in Funchal with his girlfriend, Georgina Rodriguez, and his four children.
Ronaldo, 35, will be in action when Portugal take on France in Sunday’s Nations League game in Paris.