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 person involved.
"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, 35, will be in action when Portugal take on France in Sunday's Nations League game in Paris.