The McLaren driver, who broke a rib in a crash in last month’s Australian Grand Prix, faces further tests before being given the full go-ahead.
The Spanish two-time champion, 34, will be given a second check-up after taking part in first practice on Friday.
Governing body the FIA took six hours to make this decision after testing Alonso on Thursday.
The FIA medical delegate Jean-Charles Piette barred Alonso from racing in the second race of the season in Bahrain two weeks ago because of his injuries.
Speaking before the decision was made public, Alonso said that he felt “100%” but expected the FIA to want to examine him after first practice.