Martin fell from his bike on Lap 14 of the 22-lap race and was struck by VR46 rider Fabio di Giannantonio.
The Spaniard suffered 11 broken ribs and a punctured lung.
He was treated at Hamad General Hospital and on Sunday was released.
“Finally out of the hospital,” Martin wrote on social media.
“Thank you all for the messages and for supporting me through this tough time in my life.
“I’m still in a lot of pain, but everything is under control.
“I’ll stay in Qatar for a few more days as a precaution, and as soon as I can, I’ll head home to rest and be with my people.
“Hope it’ll be very soon.”
Martin had only just returned to MotoGP after consecutive injuries ruled him out of the first three grands prix of the season.
With his latest injury, the 28-year-old could miss the first half of the season.
For the upcoming Spanish Motorcycle Grand Prix at Jerez, Martin will be replaced by Lorenzo Savadori, who will join Marco Bezzecchi.
Bezzecchi sits seventh in the championship. Apilia satellite rider Ai Ogura is ninth for Trackhouse Racing.
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