Farquhar was hospitalized after passing out in the dugout. Additional overnight testing revealed that a ruptured aneurysm caused the brain bleed. He is currently stable but in critical condition in the neurosurgical ICU unit at Rush University Medical center.
The team says it will provide updates on Farquhar's health as appropriate, but requested privacy for the family.
Farquhar faced four batters to finish the top of the sixth before he passed out after the inning. He was attended to by White Sox medical personnel and on-site emergency medical technicians.
The team said Farquhar was conscious when he was taken from Guaranteed Rate Field to the Rush University Medical Center.
"It takes your breath away a little bit, because one of your guys is there and you no have idea what was going on," White Sox manager Rick Renteria said Friday. "When one of your teammates or anybody you know has an episode, everything else you keep in perspective. Everything has its place. We're glad he was conscious when he left here."
Renteria said that Farquhar received almost immediate attention from the medical staff after passing out. He added that he and White Sox trainer Herm Schneider initially held onto Farquhar to keep him from slipping off the bench.
Farquhar, 31, was signed by the White Sox on July 24, 2017. He has played for three other teams over seven big league seasons.
Information from ESPN's Bradford Doolittle and The Associated Press was used in this report.