The 32-year-old right-hander had struggled this season with a 6.89 ERA in 15 2/3 innings.
The Cardinals acquired Broxton in a 2015 trade-deadline deal with the Milwaukee Brewers and he went 3-3 with a 2.66 ERA in 23 2/3 innings down the stretch that season. In 2016, he was 4-2 with a 4.30 ERA in 60 2/3 innings.
A two-time All-Star, Broxton has 118 career saves in 694 appearances over 13 seasons with a 3.41 ERA and 43-38 record.
The Cardinals recalled right-hander John Gant from Triple-A Memphis in a corresponding move. Gant opened the season on the 10-day disabled list with a strained right groin before being optioned to Memphis on May 16.
The Associated Press contributed to this report.