The 63-year-old underwent successful surgery at the Mayo Clinic in Rochester, Minnesota, USA, earlier this month.
News of the operation only became known after Stewart attended a media conference to announce the dismissal of Niki Lauda as team principal of Jaguar.
The Scot retired as chairman and chief executive of Jaguar Racing in 2000 after his wife and son both developed cancer but he still has connections with the team.
A spokesman for the three-time world champion told the Daily Record newspaper: "Sir Jackie Stewart had a small pre-cancerous melanoma removed in an operation three weeks ago.
"The operation was 100% successful and doctors are delighted with his progress and condition."
Stewart's wife Helen is still recovering from breast cancer and just two years ago his son, Paul, was diagnosed with cancer of the colon, which is now in remission.
Sir Jackie formed Stewart Grand Prix with Paul in 1996 but they sold the team to Ford three years ago for £60m and it became Jaguar Racing.
Paul's own battle with cancer had already caused him to step down as chief operating officer of the team.
Sir Jackie was born in Dumbartonshire as the son of a garage owner and he entered Formula One, after a spell in F3, with the BRM team in 1965.
He won his first Grand Prix that year at Monza in Italy before going on to finish third in the World Championship in his first season.
Eventually Stewart would win 27 grands prix, becoming world champion in 1969, 1971 and 1973, as well as runner-up in 1968 and 1972.
He retired before the final race of the 1973 season - which would have been his 100th grands prix - after his team-mate Francois Cevert was killed in practice.
Later Stewart became a ceaseless campaigner for driver safety and he also took up commentating and other business ventures before setting up the team with his son.