The Our Dynamic Earth science centre has received more than 2 million in state grants since 2008 but sources have now revealed bosses fear a 20 per cent cut after John Swinney's draft budget reductions were announced last month.
As part of government cuts the Office of the Chief Scientific Adviser has been slashed by 16 per cent, although the extent of the impact on science centres has not been measured.
One source involved in funding said: "Our Dynamic Earth do make a lot of money from other sources but anything around 20 per cent is a massive amount.
"If you take for example the Science Museum in London, which attracts travelling exhibitions, they can bring in grants, fundraising, corporate investment, but Our Dynamic Earth isn't really like that.
"To fill the gap they'll have to sell more tickets, attract more corporate events, which isn't exactly easy at the moment."
They added: "The fact that they're losing government funding won't give grants and foundations a huge amount of confidence."
In January 2008 the then Education Secretary Fiona Hyslop announced that funding to Our Dynamic Earth, which has faced major financial problems in the past, would be doubled to 2.3m between 2008 and 2011.
That compared with state funding of just 380,000 the year before, and came after the venue faced major financial problems in 2004, leading to a Scottish Executive bail-out of 500,000.
Following a revamp, visitor numbers began to recover and it currently attracts around 225,000 visitorsa year.
In 2009 government funding accounted for 651,000 of the centre's 4,962,000 income, however, the proportion used in 2008 and 2010 was significantly higher.
The Scottish Government said future grants would be discussed over the next few weeks and have not yet been determined, although it expected science centres could make efficiency savings without significantly affecting the service they provide.
John Simpson, chief executive of Our Dynamic Earth, said: "We understand that due to cuts in government spending, the level of grant that we might receive may reduce.
"Our Dynamic Earth will continue to utilise any funding it receives to refresh the visitor experience, but we do not expect to have any confirmation on future funding until into the early part of 2011."