Trevor Siemian will be under center, with Luke Falk elevated from the practice squad to serve as the backup.
Darnold missed practice on Wednesday because he was feeling ill. Gase said the team learned of Darnold's diagnosis later that night and he went to the second-year quarterback's home to personally deliver the news to him. The coach said Darnold's biggest concern is weight loss, adding he has already lost about five pounds.
"He's still going through some of these tests to kind of see where he is at with all this," Gase said. "I know he's out this week. Then past that, I'll have more information as we go."
The Jets have their bye in Week 4.
"I don't want to put predictions on anything," Gase said, when asked to speculate when Darnold could return. "I'm just glad we got the bye week when we do."
Gase said Darnold did not take the news well initially, but quickly regrouped and looked forward.
"The way that he reacted to it last night, he went right into 'Where's my solutions?' He moved past the bad news and went right into, 'Alright, how am I going to get myself ready for when I am able to return to where I'm not in a bad place?'" Gase said.
Darnold is coming off a mixed performance against Buffalo last week in the season opener, completing 28 of 41 passes for just 175 yards and a touchdown in the Jets' 17-16 loss.
Many view Monday night's game against Cleveland as a must-win for the Jets, given the difficulty of their schedule going forward. They travel to Super Bowl champion New England in Week 3. Then, following the bye, they play the two best teams in the NFC East, at Philadelphia and home for Dallas, before facing the Patriots at MetLife in prime time on Monday, Oct. 21.
Siemian spent his first three seasons with Denver before serving as Kirk Cousins' backup last season with Minnesota. A seventh-round pick in the 2015 draft out of Northwestern, Siemian signed a one-year, $2 million contract with the Jets as a free agent in March.
Siemian started a combined 24 games for the Broncos in 2016 and '17, throwing for nearly 5,700 yards, with 30 touchdowns and 24 interceptions.
Gase told the team about Darnold's illness on Thursday morning. He said while the news is discouraging, he and the players have every confidence in Siemian to get the job done.
"We talked about how our next-man philosophy does not waver," Gase said. "It's about everybody doing their job. That's why Trevor's here. Has a lot of experience. Has been on winning ball clubs. He has the respect of the locker room. I think guys, the reaction I got, the way the guys looked, was like 'Let's go.' There's confidence there."
The Jets' new starting quarterback said he'll be ready for Monday night.
"Yeah, just do my job, run a clean operation, and get the ball in the end zone. It's pretty simple," Siemian said. "We've been running the same schemes, the same plays, so I feel pretty comfortable with what we're doing and I'm excited to compete, for sure."
The Darnold news is just the latest in a series of stunning personnel setbacks for the Jets. They lost stud linebacker Avery Williamson to a season-ending knee injury during the preseason and announced Wednesday that starting wide receiver Quiny Enunwa's season is over due to a neck injury.
Of more pressing concern is the status of superstar running back Le'Veon Bell. The high-priced free agent signing was set to have an MRI on Thursday on his shoulder.
"I'm waiting to find out the extent of this," Gase said. "This could be just soreness. We don't think it's anything worse than that, but we're just kind of probably being a little extra cautious."
The Jets are also holding out hope that star linebacker C.J. Mosley and rookie defensive lineman Quinnen Williams will be able to play against the Browns. Mosley suffered a groin injury and Williams a sprained ankle in the opener, though Gase said both are making progress in their recoveries.
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