Oregano was severely underweight when members of the public found him at Cushendun earlier this month.
At just 15kg, Oregano weighed the same as a newborn seal, but he should have been twice that weight.
The eight-week-old pup was taken to the seal sanctuary at Exploris Aquarium, where Leslie Turner said apart from his weight problem, Oregano was in very good condition.
"He doesn't appear to have any injuries or diseases so it's mainly a matter now of treating the malnourishment and getting as much weight on him as possible," he told UTV.
Leslie believes Oregano came out of the water because he was cold, a side effect of being underweight.
"He would have hauled out to stay warm and that's where he ended up, on the beach on a nice soft bed of seaweed."
Oregano is one of up to 35 rescued seal pups that Exploris helps every year and they are fattening him up so he can go back to his normal habitat.
"It's a matter of feeding him herring every day twice a day until he reaches a weight of 45-50kg and then he will be released," explained Leslie.
Exploris plan to release Oregano into Strangford Lough and Leslie hopes he will go on "to have a happy life".
"We don't know what happens to the seals after we release them, but we have to hope that they have the skills to survive," he said.
And for anyone who happens to see a seal on the beach, Leslie has this advice: "Don't touch it.
"Don't try to put it back in the water. Leave it alone, call Exploris. We will come and look. If it needs brought into the sanctuary, we will bring it in and rehabilitate it."