At a ceremony held at Stirling Castle - where the museum is located, Prince William officially launched the Thin Red Line Appeal.
The fund-raising campaign hopes to secure backing of £4m by 2019 to redevelop the museum.
The Prince said that he was "honoured" to be the patron of the appeal.
On arrival at the ceremony, the prince was met by the Earl of Mar and Kellie, hereditary keeper of Stirling Castle, who presented him with the key to the castle.
William was then escorted around the current museum by Col AK Miller, viewing key exhibits including The Thin Red Line painting which depicts the Battle of Balaclava during the Crimean War in 1854.
He spoke with pupils from the Queen Victoria School, whose parents serve in the Armed Forces - asking them about school life, their future ambitions - and also which football team they support.
During the visit, William also met Lt Col Alexander Grant, 70, who is in a painting depicting fighting in Aden, now part of Yemen, in 1967.
Mr Grant said: "He seemed to be an extremely interested individual and easy to talk to and quite pleasant to chat with."
In a speech at the ceremony, Prince William said: "I am honoured to be patron of the Thin Red Line Appeal, to ensure that the history of one of Scotland's most iconic regiments can be preserved as part of the nation's story here in Stirling."
Col Miller said: "We were very fortunate to get Prince William as patron for the Thin Red Line Appeal."
He added that since the museum lost its Ministry of Defence funding in 2012, it has been entirely self-supporting.
The museum recently received news that it is to be supported by the Heritage Lottery Fund.
The prince said he is "confident" the £4m target is achievable.

US singer Richard Marx said last week that he had intervened to help restrain a disruptive passenger on a Korean Air flight from Hanoi to Seoul.
Crew had been "ill-trained" and "ill-equipped", Marx said.
The airlines said it would also review the use of Taser guns on board.
"Korean Air will react more firmly and actively against in-flight violence that threatens the overall safety of the flight," it said in a statement.
As part of the changes, the airline said it would be providing more training to staff and hiring more male flight attendants, making sure at least one male is on duty in the cabin for each flight, according to Reuters news agency.
Marx's wife Daisy Fuentes, who was travelling with the singer, said the staff "didn't know how to use the taser" or to secure ropes.
Taser is a brand name often used to refer to electric stun guns.
"We have decided to improve our conditions and procedure on using Taser guns to cope with violent acts and disturbances on board in a fast and efficient manner," it added, but did not elaborate on how the rules would change.
The airline said that under existing rules, stun guns were permitted for use only in "grave" situations - where the safety of a flight or the life of passengers and crew were in danger.
This meant staff had been "hesitant" to use the equipment, the carrier added.
Individual airlines have their own policies on what equipment they carry on board to restrain passengers
Most carriers contacted by the BBC were unwilling to give details of what kit this included, citing security concerns.
Prince William has launched an appeal to secure the future of the Argyll and Sutherland Highlanders Regimental Museum in Stirling.
[NEXT_CONCEPT]
Korean Air has said guidelines will be revised for crew to react "firmly and actively against in-flight violence", after facing criticism for its handling of an on-board incident.