The leaves get brown spots on them, then the leaves turn yellow and fall off. I live in Texas and we have had record rain fall this spring.
Brown Spots on the Leaves of My Fruitless Mulberry
Certified GKH Gardening Expert
The heavy rainfall may be the cause.
A well established, healthy tree should be able to withstand the flooding rains.
I would watch the tree for any additional signs of disease or insect infestations.
I do think your tree will recover.
Here are a few articles for things to watch for.