The Australian had been due to re-assess his injuries in Friday practice, but has instead been advised by his doctors to have surgery.
Honda has announced that he will leave the Czech circuit late on Thursday and return home as a result.
The 26-year-old already trails Yamaha's Jorge Lorenzo by 39 points heading into Brno.
His decision therefore effectively spells the end of his hopes of successfully defending his world championship crown before retiring at the end of the season.
Stoner suffered significant ligament damage and fractures to his right ankle in a heavy crash during qualifying for the Indianapolis Grand Prix the weekend prior to Brno.
He bravely rode in the race with a modified boot, just missing out on a podium as he finished fourth.
He had been pessimistic about his chances heading into Brno however, saying: "In Brno there are many changes in direction and a lot of right hand corners so there will be a lot of weight on my ankle and it's going to be very difficult. I'm not feeling too optimistic."
It is not yet clear how long Stoner will need to fully recover. After Brno, MotoGP's next race will be held at Misano on 16 September.
Alongside Stoner, Ducati's Nicky Hayden - another victim of Indianapolis qualifying - and Pramac Ducati rider Hector Barbera will also miss out due to injury.