There are also fears that the increases could force firms to close and put jobs at risk, according to The Times.
Edinburgh Castle’s rateable value will increase from £326,000 to almost £1.8 million under a recent revaluation carried out by the Scottish Assessors Association (SAA).
However, the Scottish parliament building’s rateable value is set to fall from £7.7 million to just under £7 million.
These values are not what the bodies will have to pay.
Payments will be calculated by multiplying the rateable value by the poundage rate, which has been cut to 46.6p by the Scottish government.
With exemptions given to charitable bodies, Edinburgh Castle’s rates will increase from £30,000 to £165,000 under the new system.
It is likely that firms will have to balance their books by increasing prices or cutting expenditure once higher rates are introduced.
Business groups have warned that many small and medium-sized companies could face bankruptcy.
Nicola Sturgeon has also been told that tourism businesses may be forced to close with jobs lost as a result of the rates rises, which are based on revaluations undertaken in 2015.
Marc Crothall, chief executive of the Scottish Tourism Alliance, has written to the first minister requesting a meeting to express his “deep concern”.
Jackie Baillie, Scottish Labour economy spokeswoman, said: “Businesses are clearly losing confidence with the SNP government.
“Ministers have a duty to engage with the business community, and with parliament, about these changes. The tourism sector is a major employer, and it would be very concerning if visitors are forced to pay higher admission fees as a result, or if jobs are put at risk.”
Under provisional figures for revaluation released by the SAA, the National Gallery is set to have its rateable value increase from £520,000 to £913,000. The National Portrait Gallery’s rateable value will rise from £415,000 to £703,000.
A spokeswoman for the National Galleries of Scotland said: “We don’t have the full detail at this stage, but any increase in our cost base is unwelcome at this moment.”
The National Galleries said that it would need more detail from the government on the rates rise before it could say if ticket prices would have to increase.
The National Museum of Scotland has a rateable value of £3.5 million and pays about £322,000 in rates. Under its revaluation to almost £5 million, it would have to pay £457,240.
The rateable value of Kelvingrove Art Gallery and Museum in Glasgow will rise from £1.35 million to £2 million.
A Scottish government spokesman said: “Rating valuation of business properties is undertaken by independent Scottish assessors, funded by local councils, not the Scottish government.
“Each council retains all the business rates revenue it collects, and it is for councils to apply rates reductions, on top of existing statutory reliefs, as they see fit.”
The government also said that half of businesses would pay no rates.