The Spaniard had managed just 20 laps on another troubled morning for the struggling giants, who lag well behind every other team on the grid in terms of mileage with the start of the season less than a month away.
Alonso received medical attention at the circuit and was then airlifted to hospital.
"Fernando Alonso's McLaren-Honda car left the track at turn three, causing the right-hand side of his car to strike the wall," McLaren said in a statement.
"He was conscious and spoke with the doctors.
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Jenson Button was already scheduled to take over from Alonso for the afternoon session having been very limited in his running on Thursday and Saturday due to a faulty seal.
It was a much more positive morning for the other Spanish driver on show as rookie Carlos Sainz Junior was fastest in the Toro Rosso in a time of 1min 25.604.