McLaren said in a statement that he was conscious and able to communicate with doctors.
The Spaniard hit the wall on the inside of the track between Turns 3 and 4 shortly before the midday lunch break. Red flags were triggered as a result, with an ambulance also dispatched to the scene.
Alonso was duly taken to the circuit's medical centre before being transferred to hospital by helicopter for further checks.
A statement from McLaren read: "Today at 12:35 CET, while testing at the Circuit de Catalunya (Barcelona), during the fourth and final day of the current test, Fernando Alonso's McLaren-Honda car left the track at Turn Three, causing the right-hand side of his car to strike the wall."
"Fernando was driven to the circuit's Medical Centre where the circuit's doctors gave him first aid. 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."
The team added that they will issue a further update in "due course".