It will be the 35th career postseason start for Verlander, who returned to the AL West-champion Astros in a trade from the New York Mets this summer.
Manager Dusty Baker made the announcement Thursday, adding that Astros left-hander Framber Valdez would start Game 2 on Sunday night.
Verlander, 40, was 13-8 with a 3.22 ERA in 27 starts this season. The three-time Cy Young Award winner was 7-3 with a 3.31 ERA in 11 starts for Houston after the trade.
Valdez, 29, was 12-11 with a 3.45 ERA in 31 starts this season. He threw a no-hitter against the Cleveland Guardians in August.
The Twins, who swept the Toronto Blue Jays in the AL Wild Card Series to advance, have not announced their starters vs. Houston.