McGreevy (3-0) allowed a run on five hits over eight innings Sunday, striking out six and earning a win over the Giants.
McGreevy is listed as the Cardinals' scheduled starting pitcher for Tuesday's game against the Rockies at Coors Field.
McGreevy (2-0) allowed two hits and struck out four without walking a batter over three scoreless innings to earn the win Wednesday over Pirates.
The Cardinals recalled McGreevy from Triple-A Memphis on Wednesday.
The Cardinals are expected to recall McGreevy from Triple-A Memphis prior to Wednesday's game against the Pirates, Katie Woo of The Athletic reports.
The Cardinals optioned McGreevy to Triple-A Memphis on Thursday.
The Cardinals selected McGreevy's contract from Triple-A Memphis on Wednesday.
The Cardinals will call up McGreevy from Triple-A Memphis to start Wednesday's game against the Rangers, Katie Woo of The Athletic reports.
McGreevy was promoted to Triple-A Memphis on Saturday, Katie Woo of The Athletic reports.
McGreevy was reassigned Saturday to minor-league camp by the Cardinals, Derrick Goold of the St. Louis Post-Dispatch reports.