The newly-opened museum made the announcement on Twitter, without specifying whether it had bought the painting at auction this month.
Media reports say it was purchased by a Saudi prince.
The work - known as Salvator Mundi (Saviour of the World) - was sold in New York for a record $450m (£341m).
It was the highest auction price for any work of art.
The unidentified buyer was involved in a bidding contest, via telephone, that lasted nearly 20 minutes.
The New York Times reported that it was bought by Saudi prince Bader bin Abdullah bin Mohammed bin Farhan al-Saud, citing documents the newspaper had reviewed.
Leonardo da Vinci died in 1519 and there are fewer than 20 of his paintings in existence.
The Louvre Abu Dhabi
The Louvre Abu Dhabi museum opened earlier this month in the United Arab Emirates.
It cost £1bn to build the museum over the past 10 years.
It holds 600 artworks permanently and 300 loaned from France. The museum pays Paris hundreds of millions of dollars for this as well as for the use of the Louvre name and managerial advice.
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