As a result of an internal investigation, one member of staff was dismissed and another has resigned.
Two members of staff from the finance department were initially suspended after the discovery of the fraud, which is understood to date back several years.
It found that more than £80,000 was missing after an investigation by accountancy firm KPMG.
A museums spokesman said: “We became aware of the issue in July 2012 and started an investigation immediately with the involvement of our internal auditors KPMG.
“Since then it has been confirmed that there has been a fraud. The matter has been passed on to Lothian and Borders Police.
“Two members of staff were suspended and following internal disciplinary procedures, one member of staff was dismissed and the other resigned.”
According to NMS accounts for 2011-2012, auditors were “engaged to review the integrity of certain cash withdrawals following discrepancies which came to light during July 2012”.
It was on the basis of this report that museum bosses decided to call in the police, who continue to investigate.
A police spokesman said: “Lothian and Borders Police can confirm that we are investigating a report of historic fraud at the National Museums of Scotland.”
Scottish Liberal Democrat leader Willie Rennie said: “The NMS does fantastic work with schools, students and the wider public to educate them about the history of Scotland.
“However, it is also a body in receipt of a substantial amount of public funding. The allegations of historic fraud that have been reported are clearly very serious.
“I know that management at NMS will be anxious to get to the bottom of this and it is right that the legal process is allowed to run its course.”
A Scottish Government spokesman said: “The National Museums of Scotland has kept the Scottish Government informed about the case.
“This case is currently being investigated by Lothian and Borders Police, therefore we are unable to comment further at this time.”
NMS receives more than £20 million a year from public funds. It runs, among others, the National Museum in Chambers Street, as well as the Museum of Flight in East Fortune.