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."

The official violated the International Paralympic Committee's (IPC) ban on political gestures.
Belarus' neighbours Russia are banned from the Games following state-sponsored doping.
"A hero has appeared amongst us," said Maria Zakharova, a spokeswoman for Russia's Foreign Ministry.
"This is the person who showed solidarity with people who were disgracefully treated in an inhumane way in not being allowed to compete at the Paralympics," Zakharova told Interfax news agency.
The official, identified by Russian media as Andrei Fomochkin, has had his accreditation for Rio cancelled by the IPC.
IPC head of media Craig Spence said: "I'd like to thank the media for ensuring there was a picture of the individual on Twitter pretty quickly. We managed to locate that individual and confiscate the flag pretty much within 20 minutes of the flag being displayed.
"It's seen as a political protest because he carried a Russian flag when he's in the Belarus delegation, and when you've got the president of the Belarus National Paralympic Committee being so vocal in the media before these Games saying he disagreed with our decision, then it's a pretty easy conclusion that it was a political protest.
"We check all teams before they go out into the stadium at every single Games, so that flag was pretty well hidden on that person because all of the Belarus team was searched before they went out and the flag was somewhere on the person that we didn't notice."
Fomochkin has received support from Belarus for his gesture.
"This was the right thing," Dmitri Mironchik, press secretary for Belarus's Foreign Ministry, told RIA Novosti. "If we need to answer for these gestures, then we will answer."

The teenager was taken to Southmead hospital with knife wounds, but died of his injuries.
Two 19-year-old men have been arrested on suspicion of murder following the stabbing on Stothard Road, Lockleaze, at about 5:50 GMT.
Avon and Somerset Police said the men remained in custody and the force is not looking for anyone else.
Officers have closed the road during investigations.
A student has pleaded for the return of her prosthetic hand after losing it on a night out.
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A Belarus official who carried a Russian flag into the opening ceremony of the Paralympic Games has been banned from the competition.
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