The Nigeria international, back at the club this summer after a difficult loan spell at Crystal Palace last season, was carried off on a stretcher in the closing stages of Thursday's match at the Stade Louis II following a heavy challenge from Monaco's Christian Mawissa, who was sent off for the foul.
According to a Getafe statement, initial examinations found a contusion to the kneecap of his right leg, easing fears of a more serious injury, though the club says further tests will be needed to determine the full extent of the damage and his eventual return date remains dependent on how the injury develops.
Uche spent last season on loan in the Premier League with Crystal Palace, making little impact under Oliver Glasner - he failed to start a single league game - before returning to Getafe this summer with his long-term future still unresolved.
The 23-year-old made 41 appearances and scored five goals for Getafe the previous campaign after joining from Ceuta, and has been the subject of interest from clubs including Real Betis and Real Sociedad as the club looks to raise funds this window.
Monaco won the match 1-0 through a Brunner penalty converted after Davinchi conceded a spot-kick, with goalkeeper Diego Ferrer denying Aleksandr Golovin from a direct free-kick either side of the incident. Getafe also lost Kiko Femenía to injury late on, leaving them to finish the game with 10 players following Mawissa's dismissal. They round off their pre-season with a trip to face Tottenham in London this Saturday.
Getafe had started the friendly the brighter of the two sides after early Monaco pressure, with Ramón Terrats and Andrés García both going close, though neither side could add to the scoreline before the late flashpoint overshadowed the result. The club will provide a further update on Uche's condition once the additional scans have been completed.