It is the second time the gallery has been shortlisted since opening in 2011.
The winning museum will be announced at a ceremony at the British Museum on Wednesday July 5. For the first time, each of the shortlisted museums will receive £10,000 as recognition of their achievements.
Simon Wallis OBE, director of The Hepworth Wakefield, said: “We are so delighted that our work throughout our fifth anniversary year has been recognised by being shortlisted for this prestigious and coveted prize.
“2016 was an exceptional year for The Hepworth Wakefield because of the number and variety of people we welcomed to experience our ambitious and intelligently popular exhibitions, valued learning opportunities and engaging public events. In particular, we are proud of the successful launch of the first Hepworth Prize for Sculpture, which did so much to reaffirm and extend Yorkshire’s position as the home of British sculpture.