The centre says it is taking up to five calls a week from owners whose terrapins are breaking the glass in the tanks meant to contain them.
The Scottish Society for the Prevention of Cruelty to Animals is keeping two large terrapins at its centre in Lothian after they were abandoned by their owners.
The SSPCA estimates that thousands of children bought the reptiles when the Ninja Turtles Raphael, Leonardo, Donnatello and Michaelangelo were at the peak of their popularity.
Then, the pets were about the size of a 50p piece, and cost just a few pounds, the same creatures have now grown many times in size.
The centre says it is taking up to five calls a week from owners whose terrapins are breaking the glass in the tanks meant to contain them.
Staff have named the rescued terrapins Raphael and Donnatello. The former was found in the shallow waters of the River Forth earlier this week, while its partner had been dumped in Edinburgh's Union Canal.
SSPCA spokeswoman, Angela Walton, said the charity was finding it almost impossible to find good homes for them.
"Raphael and Donnatello would have been bought when Ninja Turtles were all the rage, and they have obviously been abandoned.
'Cute, wee animals'
"Children were desperate for them when the Mutant Turtles were the in thing, but the same cute wee animals have grown and become very difficult to deal with.
"The wee boy who came out of the pet shop with a tiny little pet has left school, grown up and moved on, and the terrapin has become huge and too difficult to care for," she said.
"Some of them have grown so large and powerful that they are physically smashing their way out of their tanks."
Miss Walton said terrapins, which are native to South America and South Asia,
could live for up to 30 years but needed specialist care.
She added: "Like other exotic animals, terrapins are quite demanding pets.
"They are tiny at first but they grow extremely large and are also vulnerable to diseases if they are not cared for properly."
The SSPCA has encountered the effects of previous cases of Hollywood-inspired crazes.
Miss Walton added: "There has been a general explosion of exotic animals in Scotland, for which Hollywood must take part responsibility.
"Walt Disney managed to convince children chipmunks would be good pets after their cartoon characters Chip'n'Dale caught the public's imagination.
"We are still seeing the effects of Jurassic Park in terms of the number of iguanas, water dragons, chameleons and snakes abandoned after the initial fad wore off."