The 25-year-old right-hander is 3-4 with a 5.68 ERA in seven starts this season. He dazzled for the A's in September, going 2-0 with a 2.15 ERA in five starts after the trade.
Cotton allowed five home runs in his past two starts and was drubbed for seven earned runs in a loss to the Los Angeles Angels on Tuesday.
"Jharel has pitched better than what his overall line shows," A's general manager David Forst said, according to the San Francisco Chronicle. "Even on Tuesday, his stuff was excellent as evidenced by the strikeouts [seven]; he just needs some more consistency with his performance.
"The bottom line is that we currently have six starters who are probably deserving of being in the big leagues; Jharel needs to continue to improve in Nashville so he's ready when the next opportunity arises."
Right-hander Sean Manaea, who is expected to come off the disabled list on Sunday or Monday, will likely take Cotton's spot in the rotation. Manaea, 25, was placed on the 10-day disabled list on April 30.