The 64-year-old is being treated in Aberdeen Royal Infirmary for what is understood to be a heart problem.
His nephew Stephen, who pulled out of the Wales Open during his second round yesterday morning due to a back injury, said: "He is critical but stable.
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"My family is in disarray at the moment and it is obviously a worrying situation. We are all anxious."
Bathgate-born Gallacher, who lives in Berkshire, is the father of three children, the most famous of whom is TV presenter Kirsty.
George O'Grady, chief executive of the European Tour, said: "We are in touch with Bernard's wife Lesley and the Gallacher family and, obviously, we join with everyone in wishing Bernard a speedy recovery."
It is not known whether his wife Lesley, and daughter Kirsty have travelled to Scotland to be at his bedside.
Gallacher reportedly took unwell at a dinner at the Marcliffe Hotel in Aberdeen following an appearance at an event at Banchory Golf Club.
The Scottish Golf Union, the governing body for amateur golf in Scotland, was among those who passed on their best wishes.
"Our thoughts and prayers go out to Bernard Gallacher, one of Scotland's golfing greats. Let's hope for a speedy recovery," said the union.
The golf star led Europe to a dramatic victory over the United States in the Ryder Cup in 1995, having twice previously been a losing captain.
Gallacher turned professional in 1967 and was named the Sir Henry Cotton rookie of the year the following season.
In 1969 he became the youngest winner of the prestigious PGA Championship at 20 years and 97 days, a record which stood until earlier this year when rising Italian star Matteo Manassero triumphed at Wentworth aged just 20 years and 37 days.
Gallacher made the first of his eight Ryder Cup appearances as a player in 1969, defeating Lee Trevino in the singles at Birkdale in a contest which famously ended in a 16-16 draw, after Jack Nicklaus sportingly conceded a putt to Tony Jacklin on the 18th green of the final match.
The next seven contests all ended in defeat, the last coming by a single point at Palm Beach Gardens in Florida in 1983, the first time Tony Jacklin captained the European side.
Gallacher went on to captain Europe in 1991, 1993 and 1995. The first two contests ended in narrow defeats - before a memorable one-point win at Oak Hill in New York.
Gallacher went on to become a successful broadcaster and reported on last year's Miracle at Medinah Ryder Cup win for BBC Radio Five Live.