Amelia Welch, 20, from Axminster in Devon, was partying with friends in Plymouth on Friday when she lost her hand, which cost about Â£3,000.
The Plymouth University marine biology student said she only realised the cosmetic prosthetic was missing the following morning.
She thinks she could have left it in a nightclub and forgot to pick it up.
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Amelia, who was born with a congenital malformation in her right hand, said she had gone to Oceana nightclub after a university ball.
Her hand is "more functionable" without the prosthetic which has very little movement, she said.
"I do take it off to go to the toilet, but most of the time when I go out I put it on because it gives me confidence," she said.
"I must have been drunk when I took it off and forgot about it.
"I went back to halls with friends and went to bed and the next day I realised that I did not have it."
It is the first prosthetic she has had and fits on her hand "like a glove" she said.
Another one could cost as much as Â£5,000 and mean many hours of visits to orthopaedic specialists.
"Someone might have picked it up and not realised what it was," she said.
"It's worth everything to me, but nothing to anyone else."
A student has pleaded for the return of her prosthetic hand after losing it on a night out.