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.
Prince William has launched an appeal to secure the future of the Argyll and Sutherland Highlanders Regimental Museum in Stirling.