The cap, which is one of only five awarded to Baxter, was previously on display at Ibrox Stadium, the home ground of Rangers FC.
It was given to Baxter, nicknamed "Slim Jim", after the 1961-62 British Home Championship.
McTear's Auctioneers and Valuers said it is expected to fetch between £5,000 and £6,000 at its sports memorabilia sale in Glasgow on Sunday.
The footballer, who was most prominent during the 1960s, played 34 times for Scotland but only received five caps as the system at the time only awarded players one cap per season regardless of appearances.
Baxter made a total of 150 appearances for Rangers and is remembered for performing "keepy-uppy" during a game for Scotland in 1967 against England, who were the world champions at the time. He died in 2001 aged 61.
Brian Clements, from McTear's, said: "Jim Baxter is a true footballing legend and one of the greatest Scots to have played the game.
"This is the chance to get your hands on a piece of real sporting history belonging to one of the true greats.
"This cap will appeal not only to Rangers and Scotland fans, but collectors of all sports memorabilia."
Other lots at the sale will include a winner's medal given to Patrick McEvoy when Celtic claimed the 1918-19 league championship which is valued at £1,000 to £1,500.
An autographed copy of Tommy Gemmell's autobiography, signed by all of the Lisbon Lions, will also go under the hammer, as well as golf, baseball and boxing collectibles.