Alpine said Alonso was involved in a road accident but did not give further details.
Fernando is conscious and well in himself and is awaiting further medical examinations tomorrow morning, the team said in a statement. Alpine F1 Team will not make any further statement at this point in time. Further updates will be given tomorrow (Friday).
The 39-year-old Spaniard has won 32 F1 races, with 97 podium finishes. He is returning to F1 this year after retiring at the end of his final season with McLaren in 2018.
Alonso won his two world titles with French manufacturer Renault, which was re-branded as Alpine for 2021.
Preseason testing begins at the Bahrain International Circuit in Sakhir on March 12 and the first race will also be held there on March 28.