The residence -- in the exclusive Madrid suburb of La Moraleja -- was empty at the time, sources said, as Rodrygo's parents were attending the match in Seville.
Police attended and collected evidence, after being alerted by an employee of the company responsible for the house's security.
Officers found several of the residence's rooms in disorder, and it has not yet been established what was taken, sources said.
The robbery was first reported by the newspaper 20 minutos and the EFE news agency.
Rodrygo, 22, put Madrid ahead in the second minute at the La Cartuja stadium, and then restored their lead on 70 minutes after Lucas Torro had equalised for Osasuna. He was picked as the final's MVP by Spain coach Luis de la Fuente and his staff.
A number of footballers' houses have been targeted in both Madrid and Barcelona in recent years, often while the players are away taking part in games.
Karim Benzema's house was robbed in January 2022 -- having previously been the victim of a robbery in February 2019 -- while the former Real Madrid midfielder Casemiro, now of Manchester United, and Isco and winger Lucas Vazquez have all suffered break-ins.