Edgar, who is part of the Red Bull Junior Team, said on Monday that “at the present time I am simply unable to physically compete at the level required.”
He said that he needs to “take some time out to prioritise my health” but hopes to return to competition once he has recovered.
The Briton, who was a finalist in the 2021 Aston Martin Autosport BRDC Award, will be replaced at the Italian team by Oliver Rasmussen, who will line up for his second F3 campaign.
In a social media post, Edgar wrote: “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. Hope to be back soon.”
Rasmussen returns to the F3 grid having driven for HWA Racelab in 2021.
He signed with JOTA to compete in the FIA World Endurance Championship and IMSA Michelin Endurance Cup this year, but will be unable to drive in IMSA due to the “current world situation.” He will carry out a full WEC campaign alongside F3.
Rasmussen wrote on 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!
“The current world situation has prevented me from continuing in IMSA but will still remain in FIA World Endurance Championship for the rest of the championship.”
Trident team manager Giacomo Ricci said: “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.
“Oliver Rasmussen will be replacing Edgar. He is a quick and experienced driver, and we are proud to welcome him to the Trident Motorsport family. I am sure that he will quickly gain the chemistry needed to gel with the team, making the most of the four days of testing between Jerez and Barcelona, which will be followed by the round at Imola.
“We will put up our best effort to help Oliver and we are sure that he will provide a great contribution to the team.”