Following an examination at the Sakhir circuit on Thursday morning it was decided that the Spaniard had not recovered sufficiently following his crash in Australia to compete.
“Two sets of chest CT scans were compared and it was decided that there was insufficient resolution of the signs to allow him to compete on safety grounds,” read an FIA statement.
“A repeat chest scan has been requested before the Chinese Grand Prix and the results will be considered before allowing him to race there.”
The news means that McLaren reserve driver Stoffel Vandoorne will make his Grand Prix debut this weekend, replacing Alonso.
Vandoorne already has several test days under his belt with McLaren, including driving last year's MP4-30 at Paul Ricard in late January this year.
He also has previous form at Bahrain, winning there on his GP2 debut in 2014, and completing a pole/victory double at the start of his dominant title-winning campaign last year. He won again when the series returned to Sakhir at the end of November, and claimed a podium by finishing second in the sprint race - repeating the result he scored in the opening sprint race of the year.
Alonso, meanwhile, will miss a Grand Prix for the second year in succession, having been forced to sit out last year's Australian season opener - again on medical grounds - following a heavy crash during pre-season testing.