It was Cole's second start since coming off the disabled list with right shoulder fatigue. Pirates manager Clint Hurdle said after the game that the team was not "overly alarmed" about Cole's injury.
According to Singer's report, right hander Brandon Cumpton will be called up from Triple-A Indianapolis to replace Cole in the rotation and is slated to start Wednesday's game against the St. Louis Cardinals.
Cole, who the first overall pick in the 2011 MLB draft, has a 7-4 record with a 3.78 ERA in 14 starts with the Pirates this season.
Cumpton went 3-2 with a 4.61 ERA in nine starts for Pittsburgh earlier this season, and has gone 4-1 with a 1.76 ERA for Indianapolis.