Marquis, who missed two weeks of Spring Training tending to his 7-year-old daughter, who was injured in a bicycle accident, is expected to throw around 100 pitches. He allowed just one run over six innings in his first outing with New Britain.
The Twins haven't decided where Marquis will be slotted in the rotation just yet, but it could be as early as Tuesday against the Yankees in New York.
"He's game-on," Twins manager Ron Gardenhire said. "If it were up to him he'd be pitching for us tomorrow, not down there, but we're trying to do the smart thing and let him get some innings underneath his belt, as you need in Spring Training, before we throw him into the hot box here. He's pitched 13 years. He knows when he's ready. But he also knows this is the right thing now."