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The Australian contested the most recent German Grand Prix for the Japanese manufacturer after Alex Rins suffered wrist and ankle injuries at the Assen TT after a high-side.
Gardner finished 19th in his first start for the factory Yamaha team.
Crutchlow was set to race for Yamaha as a wildcard entry at his home grand prix but additional surgery on his injured wrist has slowed his recovery.
“Unfortunately, I am unable to attend my wild card appearance at the British GP at Silverstone this year,” said Crutchlow.
“I had surgery on my hand two months ago, and the recovery has not gone as expected at all, leading to a further surgery and complications. It is important to let my hand heal fully before trying to ride the MotoGP bike.
“I look forward to coming back and riding with my Yamaha Factory Racing MotoGP test team as soon as I can and continue our project to improve the current and next year’s package for the Monster Energy Yamaha MotoGP Team.
“This year we have seen some improvement already thanks to endless work from everyone at Yamaha and the team. I hope to watch an exciting British GP this year and that everyone has a great weekend!
“Finally, I would like to wish Remy good luck and to have fun. He has experience on the MotoGP bike and got a good taste of the Yamaha in Germany at the last race, so it is the perfect situation for him to ride the bike again.”
After a solitary season with the factory KTM team in 2022, Moto2 champion Gardner moved to the Superbike World Championship with Yamaha.
He finished ninth in his debut season and scored his first WSBK podium at Assen in April.
“First of all, I just want to say that I hope that Cal can get better soon. I saw him last week, and I hope he can get back to riding and help the MotoGP project along,” said Gardner.
“Obviously, it’s a nice opportunity to get to ride the M1 again, so I’m really happy.
“Silverstone is a track I like, and hopefully I can give some more important feedback to Yamaha and the team and continue to enjoy the moment.
“Thanks to everyone at Yamaha, and I’m looking forward to riding again.”
Gardner will continue his WSBK season at Autodrom Most in the Czech Republic across July 19-21 before returning to MotoGP on August 2-4 at the British Grand Prix.
Rins, who Gardner replaced in Germany, is expected to return for the upcoming Silverstone race.
