Kubica, Renault's leading driver and a race winner in Canada in 2008 with his former BMW-Sauber team, was flown to a hospital near Genoa where surgeons got to work as soon as possible.
"After undergoing extensive medical checks this morning, Robert Kubica has been diagnosed with multiple fractures to his right arm, leg and hand. He is currently undergoing surgery at the Santa Corona Hospital in Pietra Ligure," a Renault statement said.
His manager Daniele Morelli told reporters at the hospital: "Surgeons are trying to re-establish the functionality of his right hand...but Robert is very strong and he will do it." With little more than a month to go before the season-opening Bahrain Grand Prix, the 26-year-old will now almost certainly miss the start of the season and his entire career could be in jeopardy.
Renault have Brazilian Bruno Senna and France's Romain Grosjean as their official third drivers. Senna competed last season for the HRT team while Grosjean started seven races for Renault in 2009.
Neither has ever scored a point in Formula One and media reports quickly linked Germans Nick Heidfeld and Nico Hulkenberg to the possible vacant seat.
Kubica's race teammate is Russian Vitaly Petrov, who made his debut last season.
Kubica was heading to the start of the Ronde di Andora event near Genoa in a Skoda Fabia when the car went off the road and hit a church wall.
Italy's ANSA news agency said the car had been taken in by police for checks while a wet asphalt road which had tree branches sticking out was the most likely cause of the crash.
The co-driver Jacub Gerber got out unhurt while Kubica had to be extracted by firemen.
Kubica, a keen rally fan who has entered several events previously, tested the new Lotus-backed Renault in Valencia last week ahead of the Formula One season, which starts in Bahrain on March 13.
The Pole walked away virtually unscathed from a huge crash in Canada in 2007 but still bears the scars of a serious road accident as a passenger in 2003 that left him with titanium bolts in his arm.
