Drabek, 26, gave up eight runs on 10 hits in eight innings this spring for an earned-run average of 9.00 in four outings.
"He's not going to make the team," manager John Gibbons said Sunday. "He needs to go down there and get his work in."
The right-hander underwent Tommy John surgery in 2012.
Nolin, 24, had a rough start against the Tampa Bay Rays on Saturday, allowing five earned runs on five hits and three walks in 1 2/3 innings that included a grand slam homer to Mikie Mahtook.
"He's not ready to pitch in the big leagues just yet," said Gibbons. "We have high hopes for him but he wasn't ready yet."
The Jays optioned 30-year-old reliever Neil Wagner to Buffalo on Friday.
"Let's be honest, he's good enough to pitch in the big leagues," Gibbons said. "He deserves to be pitching in the big leagues. But the way we're set up now, we've got a few guys out of options, really good pitchers. Sometimes having an option works against you.
"You could say the same thing for Jenkins. He should be playing in the big leagues. They're not far away. If somebody falters ... and we feel like they can help us more, he'll be right back up. That's just the way the game works."
In five spring appearances, Wagner gave up five earned runs in 5 2/3 innings for an ERA of 7.94. Jenkins, 26, yielded three earned runs in 6 2/3 innings for an ERA of 4.05.
All four of the players sent down had options remaining.
Esmil Rogers, Todd Redmond, Jeremy Jeffress and Dustin McGowan are out of options, meaning the team could lose them if they are sent down.