The 83-year-old Hall of Famer was taken from his home by ambulance Thursday to Shands Hospital at the University of Florida, about 50 miles away.
Williams was given fluids and antibiotics in the intensive care unit, and his vital signs improved, The Boston Globe reported. His temperature was 100 degrees before he arrived, the newspaper said.
"Dad's doing all right," son John Henry Williams told the newspaper. "He's got some sort of cold or flu or something. But he's far from dead."
The family at first didn't think it was serious enough for a hospital visit, but decided not to take a chance. Williams said his father might return home Friday.
"There's no time limit," he said. "We want to make sure we know what he's got...He was probably fighting it for a few days. But this isn't a big deal."
Williams, who requires daily kidney dialysis, has been slowed by a series of strokes and congestive heart failure in recent years.
He had an especially severe stroke in 1994 that limited his vision and mobility. He also has had an increased heart rate and high blood pressure in recent years.
In November 2000, doctors placed a pacemaker in Williams' chest and two months later he had the open-heart surgery because of congestive heart failure. He spent part of his time recovering in San Diego, his hometown, and has been at his Florida home since Aug. 30, his 83rd birthday.
In a rare interview in September, the former Red Sox star told The Boston Sunday Globe, "I'm feeling pretty good."
"But my whole life has been knocked out of joint," he said. "Oh, boy. I've never been through years like I've been through in the last four years. There's nothing I can compare it to in my life. I really have been through hell."
Known during his playing days as "The Splendid Splinter," Williams has lived in Florida since retiring from the Red Sox in 1960.
The Hall of Famer played his entire 19-year career with Boston and was the last man to bat .400 for a season, hitting .406 in 1941.
By Fred Goodall © MMII The Associated Press. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed