Flaherty (4-5, 4.95 ERA) had been set to face the Chicago Cubs at London Stadium. He has made 15 starts this season.
Flaherty, 27, allowed 10 hits and six runs in each of his past two starts, though he got the win in the Cardinals' 8-6 victory at Washington on Monday.
Sunday's starter was still to be determined, Marmol said Saturday.
Reliever Jordan Hicks was unavailable because of illness. Hicks recorded the save in three straight wins this week.
Infielder Nolan Gorman also was ill but has limited availability.