Left-hander John Gast has been recalled from Triple-A Memphis and will start on Tuesday against the New York Mets.
Westbrook is 2-1 with a 1.62 ERA in six starts. In a 5-4 win over the Chicago Cubs on Wednesday, he allowed three earned runs over 5 1/3 innings.
"I don't think it is anything to be super alarmed about," Westbrook said. "It's inflamed right now. It's a precautionary type of DL stint. Hopefully, we'll knock it out."
Cardinals general manager John Mozeliak indicated that the move to the DL was, in part, a precautionary one.
"It's really not that big of a deal," Mozeliak said. "He's going to miss two starts. He should be ready after that."
The move is retroactive to Thursday.
Gast is 3-1 with a 1.16 ERA in seven starts with Memphis. He did not allow an earned run in five April starts and was named the organization's Pitcher of the Month.
Gast was drafted in the sixth round of the 2010 First-Year Player Draft. The 199th overall pick, Gast played at Florida State University.
"He's had a lot of success recently, and we want to see what he can do," Mozeliak said.
St. Louis moved Jason Motte to the 60-day disabled list. Motte underwent season-ending Tommy John surgery on Tuesday.
Steve Overbey is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.