Colbrunn is expected to remain in the hospital for about a week.
Colbrunn, 44, was complaining of a headache before Wednesday's game. It got worse throughout the day. Eventually, one of the trainers took him to the hospital, where doctors discovered he was suffering from a subarachnoid hemorrhage, which is described as bleeding between the brain and the thin tissues that cover the brain.
As far as when Colbrunn could return, there's no timetable.
"It's very serious," said Farrell. "We're hopeful he does return to us. But with the information we have now, his health is first and foremost. The timeframe will work itself out."
Farrell spoke with Colbrunn's wife earlier Friday. Colbrunn's family members are with him in Cleveland.
With Colbrunn out, Victor Rodriguez is serving as the interim hitting coach. Tim Hyers, the team's hitting coordinator, is on the staff in Colbrunn's absence.
Matthew Wentworth is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.