There had been speculation on social media surrounding the 73-year-old’s health, although no further details were given about his condition.
Smith, who had two spells managing Rangers during a managerial career that also saw him take charge of Everton between 1998 and 2002, underwent surgery earlier this week.
A statement issued by Rangers read: “Rangers Football Club can confirm Walter Smith had an operation on Monday and he is currently recovering in hospital.
"His family have requested privacy at this time."
A defender during his 14-year playing career, Smith began his senior career with Dundee United and had a loan spell with Dallas Tornado in 1967 before eventually joining Dumbarton in 1975.
He returned to Tannadice in 1977 and hung up his boots in 1980.
But he had already taken his first steps into management, coaching the Scotland Under-18s from 1978 until 1982, when he took charge of the Under-21s.
After a spell as assistant manager to Graeme Souness, Smith was named manager in 1991 and oversaw a successful seven-year spell before leaving for Goodison in 1998.
His four years on Merseyside were less remarkable and he was appointed Scotland manager after a brief stint as Alex Ferguson’s No.2 at Manchester United.
After failing to lead Scotland to the 2006 World Cup, Smith returned to Rangers in 2007 and remained there until 2011 when he retired from management.
He won 21 trophies over his two spells in Govan, entering the history books as one of the club’s most successful managers, second only to Bill Struth.