The cracked and broken tiles have been identified with yellow and black tape stuck around them to warn visitors to Kelvingrove Museum and Art Gallery of a potential trip hazard.
Some of the tiles have become cracked and loose.
Glasgow Life – Glasgow City Council's arm's length trust in charge of the city's museums and sport facilities – is tackling the problem with a programme of works, starting this week.
Replacement tiles – identical to the originals, which are more than 110 years old – have been sourced from Italy and Portugal.
The cost of replacing the 120sq mtrs of damaged tiles at the A-listed building is around £26,000 and will take at least six weeks.
It is the biggest spend on maintenance at the museum since a £35 million refurbishment in 2006.
In December last year, Kelvingrove celebrated welcoming its 10millionth visitor since its relaunch.
A spokesman for Glasgow Life said: "Kelvingrove Art Gallery and Museum has welcomed over 10 million visitors since it reopened to the public in 2006 so it is hardly surprising that the floor is seeing some wear and tear.
"In total, 120sq mtrs of floor tiles will be replaced, with work due to commence this week.
"The replacement tiles have been sourced from Italy and Portugal and Historic Scotland has been consulted with the regard to the building's A-listed status."
The art gallery and museum is home to some incredibly valuable exhibits – such as Salvador Dali's 'The Christ of St John of the Cross' – bought for just £8200 in the 1950s by Dr Tom Honeyman, then the director of Glasgow Museums.
Today, the Salvador Dali Society values the picture at more than £52m.
The damaged tiles are different shapes and colours and were manufactured and fitted more than a century ago, which made tracking down replacements a lengthy process.
Glasgow Life's team had a long search for the tiles, which feature five different types of marble.
Each of the 120sq mtrs of flooring contains nine tiles – meaning a total of 1000 tiles will be replaced starting this week.
The Glasgow Life spokesman, added: "The building has a mix of old tiles and replacements which have been fitted at various times down the years.
"That process continued through the refurbishment in 2006 and will continue as the building continues to age.
"It is impossible to tell which are originals and which are replacements.
"The damage is simply a consequence of so many millions of people walking through the building."
Historic Scotland is involved in the tile replacement process to ensure the A-listed building is given only the best of care.
A spokesman for Historic Scotland said: "Kelvingrove Museum is one of Glasgow's most spectacular A-listed buildings, enjoyed by thousands of visitors every week.
"The high-quality architectural detailing is a fundamental part of its impressive character and we support the council in ensuring that any repairs match the quality of the original work."
The museum and art gallery will remain open throughout the tile replacement work and visitors can take in a huge range of fascinating exhibits.
Among the current temporary exhibitions is Pharaoh – King of Egypt, which runs until February 24.
It showcases almost 100 objects from the British Museum's outstanding collection of ancient Egyptian artefacts, which is the largest of its kind outside of Egypt.
It includes treasures of ancient Egypt, including sculpture, bronze figures, written works on papyrus, jewellery and weapons.
Entry to Kelvingrove Art Gallery and Museum is free.