The plan was for Martin to leave the hospital later Sunday, team president Chris Antonetti said.
"To think about the progress he's made over the past week, it's been nothing short of amazing," Antonetti said. "It's beyond a relief, especially given where things were a week ago."
Martin, 30, became ill following a game on Aug. 7. Doctors determined he had a bacterial infection that entered his bloodstream and created toxins that damaged his internal organs, compromising their function.
Antonetti informed the team about Martin's condition Monday in Cincinnati. Antonetti, manager Terry Francona and several players visited the hospital after the Indians returned home, with Martin sitting up in a chair and in good spirits.
"If you didn't know anything was wrong, other than the IV he had connected, you wouldn't have known anything different," Antonetti said. "He was able to walk up and down the hallway a little bit, and every day he continues to get better. He still has progress he needs to make to get back to full health, but it's been a really encouraging week."
Martin was acquired from the Detroit Tigers on July 31 and has appeared in six games with the Indians. His wife, father and brother have joined him in Cleveland.
Antonetti said Martin is eager to return to playing baseball, but there is no set plan in place. Martin will undergo a series of checkups with doctors this week to monitor his recovery process.
"It's important to remember we don't know," Antonetti said. "We're in uncharted waters. There's no precedent you can look back to and say, 'What does a return to activity look like?' It's very much going to continue to be day to day."
Antonetti said recently that doctors haven't defined the specific type of bacteria or how it entered Martin's system.