The wooden cigar box, dated 1963, went under the hammer at Mullock's auctioneers at Ludlow Racecourse.
It is thought to have been a 35th birthday gift to Guevara, who was a key figure in the Cuban revolution, from staff in his Ministry of Industry.
"We wish you much happiness on your birthday. That it will be with health and success," says the inscription.
The box is embossed with the signature of Ernesto "Che" Guevara. It also includes a picture of the national flag and an enamelled coat of arms.
The Shropshire-based auctioneers said the box was likely to have been a gift "presented in an official capacity" because it included the ministry receiver's stamp, which was put on all correspondence taken in by the office.
A spokesman said the "unique" item, sold by an individual collector, displayed Guevara's "passion for cigars".
The guide price was £10,000 to £12,000.
A box in which Che Guevara is thought to have kept his much-loved cigars has sold for £12,000.