Herrera came out of Friday night's game against the Twins with a 3-0 count on Jorge Polanco with two on and two out in the ninth. Left-hander Scott Alexander came in and eventually secured a 7-6 win.
It was the second time in less than 10 days that the injury forced Herrera from a game in the middle of facing a hitter. Herrera also came out of the Aug. 22 game against the Rockies with two out and the bases loaded, and a 2-0 count on Pat Valaika.
"It causes me to lose control after several pitches," Herrera said on Saturday.
Kenney said the injury is something they can manage for the rest of the season.
"It's in the deep flexor in his wrist [area]," Kenney said. "Very mild strain. He's had it for a while. He has full strength. Full range of motion. When it gets tight, he loses a little bit of motor control in his fingers. Deeper into a game, 25-30 pitches, it affects him. A little bit of fluid that is affecting his nerves. What we have to do is eradicate that fluid."
Yost said he will not assign any one reliever to replace Herrera as the closer over the next few days.