The Trident driver will be replaced by 21-year-old Oliver Rasmussen.
Edgar delivered a promising start to the season in Bahrain with a best finish of P11 in the Feature Race.
Edgar said via his Instagram: “As a family, we have made the extremely difficult decision that I will not continue in the 2022 FIA F3 Championship until I am feeling well again.
“Having recently been diagnosed with Crohn’s Disease, at the present time I am simply unable to physically compete at the level required.
“Once on the correct treatment path, I will hopefully be back to full health/fitness but until then I need to take some time out to prioritise my health.
“I would especially like to thank Red Bull, Trident Motorsport and D Tolson & Sons for their unwavering support throughout what has been a challenging time.”
The Trident Team Principal Giacomo Ricci added: “It is with great regret that we say goodbye to Jonny Edgar, and we wish him the quickest possible recovery.
“Since the start of the season he was weakened by physical issues, but he fought like a lion.
“He did not back down and continued to race.
“However, his conditions necessitate a break from his competitive activity to support his recovery.
“Jonny always gave his maximum to the team, he has a fantastic family and is a wonderful guy.”
Rasmussen will step in for Edgar during his second FIA F3 campaign and will balance his single-seater efforts alongside a full LMP2 season in WEC.
The Danish driver wrote on his Instagram: “I am more than pleased and excited to announce that I will participate in the FIA F3 championship with Trident for the next few rounds.
“I really want to thank the whole Trident family for this opportunity!
“Special shout to my team Jota Sport for their continued support and allowing me to take on this fantastic opportunity! I look forward to getting back behind the wheel of the LMP2 car at Spa Francorchamps next month.
InsideF2 wish Jonny a quick recovery.
*Image credits: FIA Formula 3