Gonzalez will make his major league debut in his home state.
The Cardinals also moved pitcher Joe Kelly to the 60-day disabled list with a strained left hamstring and designated shortstop Pete Kozma for assignment.
The 22-year-old Gonzalez was the Cardinals' first-round pick - 19th overall - in the 2013 first-year player draft. He was 5-4 with a 2.08 ERA in 21 minor league starts in 2013-14.
Gonzalez won four Class 5A state championships with Rocky Mountain High School in Fort Collins, Colorado. He's the first St. Louis starter to bypass Triple-A for his debut since Cliff Politte in April 1998 against the Dodgers.