The building at Kronprinsessegade 30 which houses the museum used to be the private home of the founder and was originally bought in 1810 by his great-grandfather, C. N. David, but sold again in 1830.

In 1917 it was re-acquired by C. L. David, who took up residence in it but also made his collection available to the public at the upper floors of the building.

The museum is particularly noted for its collection of Islamic art from the 8th to the 19th century, which is one of the largest in Northern Europe.

In 2006 the museum was temporarily closed to the public when it embarked on a major refurbishment and rearrangement of the collections.

The architect Carl Petersen was responsible for the first rebuilding of the top floor, where the roof was given a steeper pitch so as to create adequate space for two large, skylighted rooms.

The walls are covered with Douglas fir and the exhibition cases were manufactured in Rudolf Rasmussen's workshop.