Spain's Alonso was on his 21st lap at the Circuit de Catalunya when his car left the track at Turn 3 and hit a wall at about 150kph per hour.
With the morning session immediately red-flagged, Alonso received urgent medical attention, with a screen placed around the accident scene.
A statement from McLaren later gave an update on the condition of the 33-year-old Alonso.
"He was conscious and spoke with the doctors. However, as per usual procedure in such circumstances, he was then airlifted to hospital where he is undergoing precautionary checks," it read.
Alonso's agent Luis Garcia Abad told AFP that he would likely remain in hospital under observation for at least 24 hours.
It was another setback for McLaren and its new MP4-30 car, which has been plagued by problems, with Jenson Button having to cut short his test session Saturday.
Button was due to take over from Alonso for the afternoon runs, but the Briton had to sit it out.
With new season set to start on March 15 in Australia, the team has only a further four-day test at the same venue later this week to sort out its problems
Alonso, who left Ferrari to join McLaren at the end of last season, has 32 career F1 wins but his two title wins date back to the 2005 and 2006 seasons.
Alonso's fellow Spaniard, rookie Carlos Sainz Junior, was fastest in the session in his Toro Rosso in a time of one minute 25.604 seconds, running on fast super-soft tires.
The afternoon session gave more clues as to the readiness of teams for the season-opener with Romain Grosjean setting the fastest time of the week of one minute 24.067 second in his Lotus, again on super-softs.
Last year's all-conquering Mercedes also had good reason to be satisfied with Nico Rosberg completing over 100 laps, with his best effort the second-best of the four-day test, despite running on slower medium compound tires.
Thursday will see F1 teams return to the circuit for the last official testing before Australia.