The 39-year-old, who won the world championship in 2005 and 2006, is set to make his return to F1 with Alpine at the season-opening Bahrain Grand Prix on March 28, after last racing in the sport three years ago.
Testing for the new season is taking place in Bahrain between March 12-14, but a source told AFP his participation is not in doubt.
“Alpine F1 Team can confirm that Fernando Alonso has been involved in a road accident while cycling in Switzerland,” Alpine said in a statement.
“Fernando is conscious and well in himself and is awaiting further medical examinations tomorrow (Friday) morning.
“Alpine F1 Team will not make any further statement at this point in time. Further updates will be given tomorrow.”
Alonso joined the outfit, re-branded from Renault F1 by the French manufacturer for the coming campaign, after competing in the Indianapolis 500, 24 Hours of Le Mans and Dakar Rally races.
According to Italian newspaper Gazzetta dello Sport, Alonso has suffered a fractured jaw, damage to his teeth and is in a hospital in Bern.
The BBC reported Alonso was hit by a car near his home in Lugano, near the Italian border.
Spanish Prime Minister Pedro Sanchez was one of many to post their support to Alonso on Twitter.
“Much strength and all the best wishes to Fernando Alonso,” he said.
“We expect the injuries from this accident to be minimal. A big hug, @alo_oficial,” he added.
“Just heard about my friend Fernando Alonso’s accident, I wish him a speedy recovery,” Yazeed Al-Rajhi, who raced against Alonso at the 2020 Dakar, posted.
“We are with you Fernando. Fuerza campeon (go champion),” Le Mans organisers, the FIA World Endurance Championship, said.
Alonso, a winner of 32 grands prix who left F1 at the end of 2018, missed the start of the 2015 season with an injury, having to sit out the Australian Grand Prix with concussion.
Frenchman Esteban Ocon, whose only F1 podium came at Sakhir last December, is Alonso’s new team-mate at Alpine.
Alonso is set to be the second-oldest member of the F1 paddock this term, behind Alfeo-Romeo’s 41-year-old Finnish driver Kimi Raikonnen.
Alonso completed a number of tests in the closing months of 2020 to prepare for his F1 comeback, making his full official testing return at the end-of-season session in Abu Dhabi in December.