The game has been rescheduled to Friday at 4:10 p.m. ET. The forecast Thursday calls for a rain-snow mix and cold conditions.
Ryan, who is 25 and was acquired last July in the trade that sent Nelson Cruz to the Rays, will be the first rookie to start for the Twins on Opening Day since Tom Hall in 1969. The right-hander was a member of the U.S. team that won a silver medal at last summer's Olympics.
The game also will mark the debuts of several other high-profile players with new teams.
Newcomers Jesse Winker, Eugenio Suarez and highly touted rookie outfielder Julio Rodriguez are expected to make their Mariners debuts, while All-Star shortstop Carlos Correa and slugging catcher Gary Sanchez will play their first game with the Twins.
Seven games remained on Thursday's schedule: Milwaukee at the Cubs, the Mets at Washington, Cleveland at Kansas City, Pittsburgh at St. Louis, Cincinnati at World Series champion Atlanta, Houston at the Angels and San Diego at Arizona.
The Associated Press contributed to this report.