The founder of the Moggery Rehoming Centre in Bristol Christine Bayka said the situation is "more serious" than it has been in the last 20 years.
On average it takes at least 10 days longer to re-home a black or black and white cat compared to a ginger one.
Following this, the centre has decided to offer free neutering for black cats to curb the number of unwanted kittens, the BBC quoted Bayka as saying.
"It's become more serious now because people live their life on selfies. Black cats are now less popular because they don't show up well in pictures," she said.
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"When people ring me in the kitten season they will say 'any colour except black'."
All 40 of the shelter's "long termers" are currently black, including Velvet, who has been at the centre for 14 years.
Bayka said she has also had people reject round-faced kittens in favour of "pointy noses".
Bayka said finding a friendly feline should be the "most important thing".
The The Royal Society for the Prevention of Cruelty to Animals (RSPCA) said it sees more black and black and white cats come into its care than any other colour of feline.
Meanwhile, Twitter users have been quick to defend their feline friends, with many proving just how photogenic darker cats can be.
RSPCA scientific officer Dr Jane Tyson urged people to look beyond what an animal looks like.
"Their fur colour makes no difference to how much love they have to give," she said.