The small mammal was spotted at 0300 (BST) on Monday by the zoo's night security as it climbed a tree. Staff in the on-site living quarters stayed under the tree to monitor the escapee during the night.
By dawn, they made an unsuccessful attempt to coax the male red panda down. Eventually a tranquiliser was used and he was brought to safety.
The zoo has ordered an inquiry to work out how the animal escaped. Martin Ellerbeck, a cameraman and director who lives near the park, saw the zoo-keepers with the red panda.
He said: "It looked pretty much under control. There were lots of people and it looked like a jovial atmosphere. "I could not really see it. There was lots of police but I do not think it was going to attack anyone."