The 10 kittens, who appear to be between six and eight weeks old, were well fed and healthy, according to Henrico Humane Society cat manager Kate Walser.
Walser said the area where the kittens were discovered is a known feral cat colony.
She said whoever left the kittens there probably knew the animals would be found and cared for.
Someone wrote a note on the lid of the bin where the kittens were stashed:
"I'm pour [sic]. Can you ladys [sic] please please help these babys [sic]?
Walser said her group was able to find other shelters and animal rescue groups to care for the kittens. She said it is kitten season and many shelters are at their kitten capacity.
The kittens are too young to be adopted by families.
Walser said cat owners who find themselves unable to care for their pets should never abandon them like this.
"Talk to your animal control, call rescue groups, but dumping them is not the way to do it," she said.
Walser added the importance of having your pet spayed or neutered. She said several groups offer low-cost options for people who cannot afford to pay full price for the procedure.