The Astros have already lost starter Framber Valdez for an indefinite period of time after the left-hander suffered a fractured left ring finger during his spring training debut on Tuesday.
Houston also is without ace Justin Verlander, who likely will miss the entire season after having Tommy John surgery on Sept. 30.
After accepting a one-year, $17.8 million qualifying offer from the Minnesota Twins last offseason, Odorizzi, who turns 31 on March 27, was limited to four starts in 2020 due to bruised ribs and a blister, going 0-1 with a 6.59 ERA in 13⅔ innings.
His lost season began when he was drilled in the side by a line drive off the bat of Kansas City's Alex Gordon in his third start. He returned in September, only to leave after 3⅔ innings with blister issues in what would be his final outing of the season.
Odorizzi went 15-7 with a 3.51 ERA in 30 starts in 2019 as he earned his first All-Star selection. He set career highs for wins and strikeouts (178) as the Twins racked up 101 wins and claimed their first division title since 2010.
He was drafted by the Milwaukee Brewers with the 32nd overall pick in 2008. He made his debut with the Kansas City Royals in 2012 before being dealt the next season to the Tampa Bay Rays with Mike Montgomery and Wil Myers in the seven-player trade that sent James Shields and Wade Davis to the Royals. He was traded to Minnesota before the 2018 season after logging four solid years as a starter for the Rays.
Odorizzi has gone 62-56 with a 3.92 ERA and 995 strikeouts in 1,042⅓ major league innings.