The hospital’s Chapel of St Luke has loaned four pieces to the Pallant House Gallery in Chichester, West Sussex.
Piper, who was one of the leading Modern British artists of the 20th Century, designed the striking tapestries in the 1980s.
They feature foliate heads, which were a common medieval symbol of the Resurrection, and are themed on the four seasons.
Piper is best known for his paintings of Britain’s romantic heritage including churches, country houses and the wartime ruins of Coventry Cathedral.
In the post-war period he was also recognised as a skilled designer of theatre sets, stained glass windows and textiles.
The Chapel’s Assistant Chaplain, the Reverend Judy Edwards, said: “We were delighted to loan the tapestries to Pallant House Gallery for their exhibition.
“I would like to assure both patients and staff that they will be back in the Chapel in June.”
John Piper: The Fabric of Modernism runs from March 12 until June 12 at the Pallant House Gallery Chichester.
For more information visit www.pallant.org.uk