The star of cult classic Four Weddings and a Funeral warned it would be a “bleak day” for the Highlands if the Army pulls out of Fort George for the first time in 250 years.
Mr Grant’s grandfather, Colonel James Murray Grant, was from Inverness and held the role of depot commander at Fort George, Highlands, after World War II.
And his father Captain James Murray Grant also served in the military as a Seaforth Highlander.
It was revealed last week that the barracks, near Inverness, were facing a fresh threat of closure by the Ministry of Defence (MOD).
Fears have been raised that any withdrawal from the site by the Army could threaten the future of the Highlanders Museum, which is also based at Fort George.
In 2011, Grant launched a public appeal to help raise £3million to redevelop the museum with the work completed two years later.
In a statement, he said: “I’m horrified to hear that there may be plans to close Fort George.
“My grandfather was commander there after the war, and I’ve been a keen supporter of the museum, which has only just been renovated.
“It would be a bleak day for the Highlands if this rumour about closure turned out to be true.”
The base was first built after the Battle of Culloden and has been the home of the famous 500-strong Black Watch battalion for almost a decade.
It attracts 55,000 visitors each year, and studies carried out into its economic impact have revealed that its closure could cost the Highlands £14 million a year and lead to the loss of 112 jobs.
Economy Secretary Keith Brown recently learned about the closure plans and has written to UK Defence Secretary Michael Fallon to say he is “disappointed” by the move - and that it would have “huge significance” for Scotland.
Fort George was previously considered for closure in a 2011 review but was spared the axe.
Inverness MP Drew Hendry has demanded talks with UK Government ministers over the future of the base.
He said: “I welcome the intervention of Hugh Grant. He has been a long-time supporter of Fort George and its history.
“I think we all agree that for Fort George to be on any list facing closure would be a disgraceful act by the Ministry of Defence and the UK Government.”
Scottish Liberal Democrat leader Willie Rennie and the SNP’s leader at Westminster Angus Robertson have both backed a campaign to save the barracks.
The MOD is reviewing its estate as it attempts to save £1 billion by cutting the size of its footprint by 30 per cent.
It is expected to reveal its full plans this autumn.
An MOD spokeswoman said: “As part of an ongoing review, we are aiming to create a smaller and better defence estate that effectively supports our Armed Forces in the important role they play.
“The MOD is considering how it might achieve this and no final decision about the future of Fort George has been made at this time.”