Farquhar, 31, passed out in the sixth inning and was helped by team medical personnel and on-site EMTs. He regained consciousness before he was taken to a hospital by ambulance.
The White Sox announced Saturday that additional testing revealed the brain hemorrhage was caused by a ruptured aneurysm. Farquhar was receiving treatment and being closely monitored in the neurosurgical ICU unit at Rush University Medical Center.
Manager Rick Renteria met with players before Saturday's game against Houston and updated them on Farquhar's condition. Asked if the right-hander required surgery, Renteria said, "We'll see how they proceed, and hopefully the outcome is a positive one."
The team says it will provide updates on Farquhar's health as appropriate, but requested privacy for the family.
Renteria said Saturday that Farquhar "had a strong heartbeat, a good pulse and was breathing well'' when he left Guaranteed Rate Field after passing out. Renteria said no one on the team saw advance signs that Farquhar might be suffering from the condition.
"Nothing really matters baseballwise when something like that happens," White Sox pitcher James Shields said. "When one of your brothers goes down, it's not very fun to watch. He's such a resilient human being. We are praying for him. We hope everything goes well.
"He's got a long way to go and he's fighting. One thing we know in this clubhouse is Farky is a fighter."
The White Sox hung Farquhar's jersey in their bullpen, and some players showed support for their teammate by adding his name and No. 43 on their caps for Saturday's game.
For Danny. pic.twitter.com/hi1PGX30i8— Chicago White Sox (@whitesox) April 21, 2018
The Tampa Bay Rays, with whom Farquhar played in 2017, did the same Sunday.
You're in our thoughts, Danny. pic.twitter.com/IjkyVkrlid— Tampa Bay Rays (@RaysBaseball) April 22, 2018
Farquhar's diagnosis stunned the White Sox, but Renteria said it didn't affect his players once the game started.
"I didn't see any of them putting their head down,'' Renteria said. "I thought they were actually were trying to play for him a little bit today.''
Houston manager A.J. Hinch said some of his players saw Farquhar collapse.
"We could see across the way that something was going on,'' he said. "As the group went around him, it just became a scary scene.''
Farquhar got two outs to finish the sixth against Houston. He fainted moments later.
Renteria said that Farquhar received almost immediate attention from the medical staff. He added that he and White Sox trainer Herm Schneider initially held on to Farquhar to keep him from slipping off the bench.
Farquhar was signed by the White Sox on July 24, 2017. He has played for three other teams over seven big league seasons.
Farquhar was selected by Toronto in the 10th round of the 2008 draft and made his major league debut with the Blue Jays in 2011. The right-hander is 10-15 with a 3.93 ERA in 253 career relief appearances with Toronto, Seattle, Tampa Bay and Chicago.
The White Sox placed Farquhar on the 10-day disabled list before the second game of their weekend set against Houston. Right-hander Gregory Infante was recalled from Triple-A Charlotte. Infante pitched a scoreless seventh and eighth innings in the White Sox's 10-1 loss to the Astros on Saturday.
Information from ESPN's Bradford Doolittle and The Associated Press was used in this report.