London and New York-based art dealers Oliver Forge and Brendan Lynch have sold the c.1938-1850BC stele for in excess of £40,000.
The 16in (41cm) high stele had previously been sold in Frankfurt in 1976 and was in a private German collection until 2016.
It shows a husband and wife holding hands and standing before a table laden with food and drink. It also includes an inscription in hieroglyphic and hieratic text reading “(O) Horus, Great of Respect. I am a falcon of gold I am”.
Forge and Lynch said a similar example, possibly by the same hand, is in the Rijksmuseum van Oudheden, Leiden, Netherlands.
The Munich museum has purchased the stele because it fills a gap in the collection and will be shown together with another stele and two statues from the same period, enabling the museum to illustrate the complete story of the First Intermediate Period through to and including the Middle Kingdom.