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.
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.