Flaherty did not factor into the decision Tuesday, allowing one run on five hits and a walk while striking out three over 5.2 innings against the Twins.
Martinez (lat) will not be activated from the disabled list over the weekend when first eligible, Mark Saxon of The Athletic St. Louis reports.
Fowler is not in the lineup for Tuesday's game against the Twins.
Flaherty was recalled from Triple-A Memphis on Tuesday and will start against the Twins the same day.
Wainwright (elbow) was placed on the 10-day disabled list Tuesday.
Flaherty, who'll be recalled Tuesday from Triple-A Memphis for his third spot start of the season, could remain with the big-league club for an extended period, Derrick Goold of the St. Louis Post-Dispatch reports.
Fowler, who's slashing .146/.257/.285 over his first 152 plate appearances, is putting in extra time in the batting cage as part of his attempt to improve his production at the plate, Derrick Goold of the St. Louis Post-Dispatch reports. "I am not liking playing poorly," Fowler said. "At the end of the day you get in there and you need that - at-bats. You can fix stuff in the cage but need it in the game. Which is not going to happen overnight."
O'Neill went 2-for-3 with a pair of solo home runs for Triple-A Memphis in its 2-1 win over Nashville on Monday.
Reyes (elbow) struck out 12 over five scoreless innings Monday in a rehab start for Low-A Peoria.
O'Neill went 3-for-8 with two home runs and four RBI for Triple-A Memphis in two games against Nashville on Saturday and Sunday.
Cecil (shoulder) fired a perfect 1.2 innings in which he recorded two strikeouts over two outings against the Padres on Saturday and Sunday.
Bader went 2-for-4 with two RBI from a triple, a solo home run and two runs in a loss to the Padres on Sunday.
Wainwright, who gave up two earned runs in 2.1 innings Sunday against the Padres, reaggravated his elbow injury during one of his last warmup pitches, which is why he was unable to execute his pitches, FOX Sports Midwest reports. "I need to pause and get it right," Wainwright said. "If I'm going to be a force down the stretch, I need to get healthy first."
Gyorko will start at third base and bat fifth Sunday against the Padres.
Fowler is not in the lineup Sunday against the Padres.
Carpenter is not in the lineup Sunday against the Padres.
Wainwright (elbow) was activated from the 10-day disabled list prior to his Sunday start against the Padres.
Martinez (lat), who went on the disabled list Thursday, is not yet participating in any type of physical activity, Jay Paris of MLB.com reports.
Wong is not in the lineup for Saturday's game against San Diego.
Carpenter is not in the lineup for Saturday's game against the Padres.
Bader went 1-for-5 with a solo home run in a win over the Padres on Friday.
Pham went 3-for-5 with a two-run home run and also was caught stealing in his only attempt in a win over the Padres on Friday.
Gant tossed a scoreless inning in relief during Friday's 9-5 win over the Padres and is expected to remain in the bullpen for the foreseeable future, Derrick Goold of the St. Louis Post-Dispatch reports.
Flaherty will be recalled from Triple-A Memphis and start for the Cardinals against the Twins on Tuesday, Jim Hayes of FOX Sports Midwest reports.
Wainwright (elbow) will start Sunday against the Padres, Jim Hayes of FOX Sports Midwest reports.