Team officials said Bechler was declared dead at 10:10 a.m. (1510 GMT).
Teammates were updated on Bechler's condition during a clubhouse meeting before taking the field for Monday's workout. They were summoned inside at 10:30 a.m. and told of his death.
Bechler made his major league debut last year, going 0-0 with a 13.50 ERA in three relief appearances. He was expected to begin this season with the club's new Triple-A affiliate in Ottawa.
Bechler was chosen in the third round of the 1998 draft out of South Medford High School in Oregon. He spent most of last season at Triple-A Rochester, going 6-11 with a 4.09 ERA in 24 starts.
Called up to the majors late in the year, he made his debut Sept. 6 against the Anaheim Angels.
Bechler was the second baseball player to die suddenly in the past year. Last season, St. Louis Cardinals pitcher Darryl Kile, 33, died in his sleep while in Chicago for a game against the Cubs. An autopsy revealed he had severe arterial blockage.
He was at least the second professional athlete in the past two years to succumb after taking ill at a pre-season practice. In 2001, Minnesota Vikings lineman Corey Stringer died after collapsing at a practice.