The attraction is one of 10 in the running for the Art Prize 2012, the UK's annual museum-of-the-year award and the biggest prize for arts and cultural organisations in the country.
The winner of the £100,000 top prize will be announced at a ceremony at the British Museum, in London, in June.
Glasgow's new transport museum, which replaced the popular visitor attraction at Kelvin Hall, opened last June.
The £74million structure on the banks of the Clyde has already attracted more than 1.3million visitors.
Riverside is up against the National Galleries of Scotland and the National Museum of Scotland, both in Edinburgh, as well as seven other museums in other parts of the UK.
Glasgow City Council leader Gordon Matheson said: "The Riverside Museum cements Glasgow's reputation as Scotland's cultural powerhouse.
"The iconic building on the banks of the Clyde celebrates the transport, industrial and engineering heritage that helped to build Glasgow and the world.
"We are rightly proud the museum has been shortlisted for such a prestigious prize and I hope everyone will get behind one of the jewels in Glasgow's cultural crown."
Lord Smith of Finsbury, who chairs the judges panel, admitted it had been a struggle to draw up a shortlist of contenders.
He said: "Whittling the achievements of Britain's museums over the past year down to a list of 10 was unbelievably challenging.
"However, the outstanding quality of the projects we finally settled on perfectly encapsulates the vitality and dynamism of a part of our nation's cultural life that continues to innovate, push boundaries and engage the public, even in these straitened times."
Lord Smith and his fellow judges visited Riverside as it was packed with families enjoying the Easter break.
The Art Fund Prize rewards excellence and innovation in museum projects completed or undertaken in 2011.
Riverside manager Lawrence Fitzgerald said: "We were delighted to play host to the judges and share with them our vision of a transport museum which is not just about trains, trams and ships, but the stories of the people who built and used them.
"That more than 1.3million visitors have enjoyed the museum is proof we have succeeded in creating an attraction which makes an emotional connection between objects from the past and the people of today."
Last week there was a shock when it was revealed Riverside had not been included in the shortlist for the Royal Incorporation of Architects in Scotland award.