Martinez, 22, competed for the team's fifth starter spot in spring training, but lost the job to the currently injured Joe Kelly. He has instead been working as a late-inning reliever this season, the same role he held during the club's postseason run last fall.
In 30 relief appearances this season, Martinez has a 4.67 ERA and a 1.30 WHIP in 34.2 innings. He's thrown multiple innings in five of his last seven appearances, though he has yet to throw more than 2 2/3 innings or 47 pitches in a game this season.
Wainwright is only expected to miss one start. The Cardinals open a three-game series with the Mets in St. Louis on Monday.