Right-hander Jordan Lyles will be called up to start Sunday's series finale against the Reds. Bud Norris will start Monday's series opener in New York, followed by J.A. Happ on Tuesday in what would have been Weiland's spot. Wandy Rodriguez, Friday night's winning pitcher, will start on Wednesday.
A corresponding roster move will be made Sunday to make room for Lyles. Happ and Norris are each pushed back a day.
"Everything's fine with those guys ... we just give them an extra day," Mills said. "We thought this would be best."
Lyles is 4-0 with a 3.46 ERA in four starts. He has struck out 24 batters in 26 innings and walked only four. He made 20 appearances, including 15 starts for Houston last year, going 2-8 with a 5.26 ERA.
Lyles is expected to join the club in Cincinnati on Saturday.
Weiland was placed on the 15-day disabled list for a sore right shoulder retroactive to April 25, general manager Jeff Luhnow announced early Friday.
"Everything was structurally sound with his shoulder. That's always a good thing," Mills said of Weiland. "We think he's probably going to need the full two weeks."