Melissa Laurie, 28, was dragged underwater after being attacked while swimming at night with her twin Georgia.
She was able to escape the predator while carrying Melissa and managed to swim to the boat.
The women’s mother Sue Laurie told the Mail Online: “We have twin daughters who are travelling around Mexico and were attacked by a crocodile last night.
“Melissa is alive, but we don’t know if her injuries are life-threatening or not.
“She has water on her lungs and she has been coughing up blood. So we don’t know if she has a punctured lung or not. She has been put into a medically induced coma.”
Mrs Laurie, from Sandhurst in Berkshire, said both girls have been left with “terrible bite marks”.
Their father Sean added: “They were swimming after dark in the bioluminescent waters when Georgia heard Melissa cry out.
“She called for her but she didn't reply. She could hear other members of the tour group but not did not hear anything from her sister.
“After several minutes she found Melissa floating face down on the surface. But when she was bringing her back to the boat the crocodile attacked again.
“Georgia had to fight it off. She kept punching it in the head. She suffered lacerations, bite wounds too.”
Swimmers who visit the Manialtepec Lagoon are warned that crocodiles that can grow up to ten feet long live in the water.
Despite the warnings, the twins’ dad said they had been assured by the tour company that there were no crocodiles in the water.
The twins have been travelling the world since leaving the UK in March - however, their parents are now considering flying out to Mexico to bring them home.
The women’s older sister Hana Laurie launched a fundraiser to cover the costs of both parents traveling to the Central American country.
She wrote: “My family are overwhelmed with pride that Georgia managed to take the brave action she did, but now are faced with the difficulty of travelling to Mexico to support them and pay for their medical care.
“There as yet isn't clarification on how much we'll need, but already it feels very overwhelming.”
She added: “Mel and Georgia are in real need of their parents, and the most amazing medical assistance we can get to turn this awful accident away from tragedy.”
A Foreign Office spokesperson said: “We are supporting the family of two British women who are in hospital in Mexico, and are in contact with the local authorities.”