Cueto will not rejoin the starting rotation right away, the Miami Herald reported.
Cueto departed his Marlins debut April 3 with a biceps issue after giving up four runs in one inning against the Minnesota Twins, including two home runs. He went on a rehab assignment May 6 with Triple-A Jacksonville but came away with a left ankle sprain.
He is 0-1 with a 36.00 ERA on the season.
In 16 major league seasons with five teams, Cueto is 143-108 with a 3.46 ERA in 356 appearances (354 starts). The two-time All-Star has finished in the top six of Cy Young Award voting three times, including a second-place finish in 2014 with the Cincinnati Reds.
Reynolds did not make an appearance while with the Marlins.