From next month, The Riversider 100 will be withdrawn, as a result of dwindling customer numbers.
The service was introduced by transport giant First Glasgow, when the museum opened in 2011, but now it is being scrapped because too few visitors use the No 100 bus.
Operating every 30 minutes throughout the day, the Riversider connects the city centre, leaving from George Square, with the Riverside Museum and the SECC.
In November, the Riverside Museum hit the two million visitor mark, just 16 months after opening its doors, making it the most popular attraction in Glasgow.
This compares to the 460,000 people who visited the former Transport Museum at the Kelvin Hall each year.
In one day in June last year, it was visited by more than 15,000 people.
A spokeswoman for First Glasgow said: "The last day of operation for the Riversider service 100 will be Sunday, February 3.
"Before this service was launched, in May 2011, Glasgow City Council had intended to financially support a service to help get it off the ground.
"First offered to operate the service without this support on a six-month trial basis and during the first few months of the museum opening passenger numbers were encouraging.
"Unfortunately, this dropped off after a few months and service 100 has been operating at a loss since then.
"The City Sightseeing bus tour operates on this route and so the public transport link with be maintained."
The £74million museum has more than 3000 exhibits, including 150 interactive displays.
From massive steam locomotives to a recreation of a city street during the 1900s, the museum showcases the innovation of Glasgow's pioneering engineers.
Highlights at the famous attraction include a wall of cars, a hanging bicycle velodrome, a display of motorbikes and a huge steam locomotive.
A spokesman for the museum's operator, Glasgow Life, said: "The Riversider Service has been a great success and we're grateful for the support from First Glasgow for providing this extra service when the museum enjoyed such spectacular success with visitor numbers which exceeded all expectations.
"With an increase in car parking spaces and more visitors using the already strong public transport connections, we're confident that the Riverside Museum will continue to be one of the city's most popular attractions."