"We are pleased to confirm that Fernando Alonso has now left hospital. He has returned to his family's home in Spain for further rest and recuperation," McLaren said in a statement.
The Woking-based team also confirmed that Alonso will not drive in this week's final four-day pre-season test, which begins in Barcelona on Thursday.
"As a result, he will sit out this week's final winter test, at which he was due to share driving duties with Jenson Button.
Alonso crashed into a wall after completing just 20 laps on Sunday and was airlifted to hospital under sedation.
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The 33-year-old Spaniard suffered concussion but McLaren said scans on the 2005 and 2006 world champion were "completely normal."
The team blamed unusually strong winds for the crash and categorically denied there had been any mechanical failure with their MP4-30 car.
McLaren have suffered numerous setbacks in testing ahead of the new season, which gets underway with the Australian Grand Prix on March 15.
After eight days of testing, McLaren have completed less than half the mileage of every other team on the grid and nearly five times less than reigning champions Mercedes.