The cigar is part of a large collection of nearly 1,000 Brunel objects donated to the SS Great Britain Trust by collector Clive Richards.
The artefacts will join thousands more at the Being Brunel museum, which is due to open in 2016 at Brunel's SS Great Britain in Bristol. Brunel, who smoked 40 cigars a day, was one of the most ingenious and prolific engineers in history, building 25 railway lines, more than 100 bridges and three ships. He suffered with kidney problems for several years before dying of a stroke at 53 in 1859.
Matthew Tanner, chief executive of the SS Great Britain Trust, said Being Brunel would engage people of all ages by looking into the mind of a genius.