Four steel columns need to be installed at Scarthin Books, in Cromford, Derbyshire, to support the weight of about 100,000 books over four floors.
A crowd funding appeal began on Sunday and more than £5,000 has been raised.
Manager David Booker said building work was put off in favour of restocking during the shop's 41 years.
The shop, which has four floors and a vegetarian cafe, was dubbed one of the best in the world by The Guardian, in 2008.
It was also used as a set for the film When Did You Last See Your Father, in 2007.
However, a number of cracks have appeared on the walls and the staircases between floors are bowing.
Mr Booker said customers have often questioned how the bookshop "has stayed upright" and after a survey by a structural engineer, fears were realised.
"He said we needed to do some fairly sharpish structural work," said Mr Booker.
"It's a bill we could do without as an independent bookshop with tight financial constraints."
He said despite the costs of its upkeep moving out of the building had never been a consideration.
"The building itself is more than half of the overall character of Scarthin itself... people travel from far and wide.
"It's our priority to make sure this place stays standing for another 40 years."
The appeal has raised £5,510 in three days by the shop's customers who will receive a number of rewards in return.

The Boeing 767 bound for Miami experienced an "uncontained engine failure", officials involved in the investigation said.
The pilot aborted the take-off and evacuated everyone on board via emergency chutes as black smoke billowed from the plane.
Twenty people suffered minor injuries, the fire department said.
Nine crew members and 161 passengers were on board.
A federal official quoted by the Associated Press news agency said the plane appeared to have suffered a rare and serious type of engine failure in which parts break off and are spewed outside the engine.
Passengers reported an explosion followed by flames and black smoke as the plane was speeding down the runway.
Sarah Ahmed said everyone on the right side of the plane rushed from their seats and moved to the left side.
"People are yelling, 'Open the door! Open the door!' Everyone's screaming and jumping on top of each other to open the door," she told WLS-TV.
"Within that time, I think it was seven seconds, there was smoke in the plane and the fire is right up against the windows, and it's melting the windows."
The incident took place at 14:35 local time (19:35 GMT).
An initial statement by Federal Aviation Administration (FAA) said the plane had burst a tyre, but that information was later deleted from the statement.
Why do people grab their bags after a plane crash?
American Airlines said passengers who still wanted to travel had been put on another flight to Miami.
Elsewhere, a FedEx plane caught fire at Fort Lauderdale, Florida, airport after its landing gear collapsed on landing, the FAA said.

Barbara Stensland, 43, from Cardiff, went to Carmarthen on 5 August.
When she tried to get a taxi from the railway station to the venue, less than one mile (1.6km) away, she was refused.
Carmarthenshire council's senior licensing officer, Justin Power, said: "We will investigate this matter and take any necessary steps."
Ms Stensland told BBC Radio Cymru's Post Cyntaf programme it took her more than an hour to reach the venue.
She said: "I went to the first taxi in the queue outside the station, I told him where I wanted to go.
"He laughed. I thought he was just joking along because I knew it was a fairly short distance.
"When I said 'seriously, can I get in the taxi?' He said 'no, I'm not taking you.' So he pointed me helpfully in the right direction and told me to walk."
Urtha Felda, from MS Society Cymru, said: "We have heard of people having trouble getting taxis.
"If somebody's still walking you can't see that they're disabled - if someone's in a wheelchair it's really obvious.
"It's not obvious, so I would say to people - don't make judgements."
A bookshop once named as one of the best in the world could fall down unless £10,000 can be raised for structural repairs, say its owners.
[NEXT_CONCEPT]
An American Airlines plane has caught fire on the runway of Chicago's O'Hare airport while taking off.
[NEXT_CONCEPT]
A woman with multiple sclerosis has said she was refused a taxi to a meeting of the MS Society because the journey was too short.