The Lancastria troopship was carrying between 6,000 and 9,000 people when it was sunk by German dive bombers on 17 June 1940.
Only about 2,500 people survived in the largest single loss of life for British forces in the whole of World War II.
Relatives and survivors have until 15 May to apply for a commemorative medal.
The Scottish government commissioned a medal in 2008, issuing more than 375 since.
The upcoming 75th anniversary of the event signals the closure of the commemorative medal application process.
The Lancastria, a converted Cunard liner built on the Clyde, was carrying servicemen - including about 400 Scots - and a number of civilian women and children when it was bombed by German planes, sinking within minutes off the coast of France.
At the time news of the disaster was suppressed by the British government because of the impact it might have on the country's morale.
Nearly six weeks later the New York Times broke the story, printing dramatic pictures of the disaster.
Veterans' Secretary Keith Brown said: "We in Scotland feel a strong bond with the servicemen and women who have served us throughout the years and continue to protect the democratic freedoms we still enjoy today.
"The commemorative HMS Lancastria medal from the Scottish government is a lasting reminder of our gratitude to those who made the ultimate sacrifice on that fateful day. Their memory is honoured, their place in history is secured."
Mr Brown appealed for anyone who believes they or a family member is entitled to a medal to come forward and make a claim.
Survivors and descendants of those killed during Britain's worst ever maritime disaster are being urged to claim medals honouring them.