Hahn, 25, left the team Thursday to return to the Bay Area for an MRI, which revealed no structural damage to his sore right elbow -- welcoming news to a pitcher who already underwent Tommy John surgery in 2010.
He's 6-6 with a 3.35 ERA in 16 starts this season.
"He's been feeling it a little bit," A's manager Bob Melvin said. "At this time in the season, starters that have logged their innings have their aches and pains, and that's what this is right now. But it wasn't getting better to the fashion where we were comfortable with him making another start, so we'll try to be proactive here and give him some time off."
The loss of Hahn, who will miss at least a handful of starts, is alleviated by Bassitt's improved performance. The righty walked nine batters in 10 2/3 innings out of the bullpen in his first stint with the A's this year before returning to pitch in place of Gray on June 30.
He limited the Rockies to one run over five innings and, on July 5, held the Mariners to two runs in 5 2/3 innings. He has not pitched in a game since then.
"I'm a lot more comfortable here now," said Bassitt, who joined the team in Cleveland on Friday from Triple-A Nashville. "We changed some things mechanically that I do, a lot less with my hands. I keep my hands a lot closer to my chest, which really helps me. I'm throwing a lot more strikes, not walking nearly as many guys, and it seems like everything's been clicking from there."
Despite spending a month with the White Sox last year, he never faced the Indians, who will counter with right-hander Carlos Carrasco on Saturday.
"The depth that we've acquired this offseason with the starting pitching shows up in times like this," Melvin said. "Not only that, Chris has pitched really well for us the last two times out, so he should come here with a good deal of confidence."
• Left-hander Sean Doolittle (shoulder strain) played catch out to 75 feet Thursday and "feels good," Melvin said.
• Switch-pitcher Pat Venditte is scheduled to throw his first bullpen on Thursday since hitting the DL with a right shoulder strain on June 12.