Historian Hugo Vickers said the permission may also have been granted because Harry has retired from active service.
British Army rules do not usually allow beards, except in rare circumstances, such as because of skin complaints, or for religious reasons.
Pioneer Sergeants are the only rank allowed to have a beard, although members of the Special Forces can when behind enemy lines.
Harry is, however, no longer a serving officer and therefore military rules may not apply to him.
A bearded royal bridegroom is a rarity. Indeed none of the current Royal Family sported facial hair on their own wedding days.
But the Queen's grandfather, George V, did have a beard when he married Mary of Teck.
Mr Vickers said: 'Theoretically the Army don't like it which is why at one point he took the Salute at Sandhurst in a suit.'
In December, Harry wore a dark suit and overcoat, with medals on the outside, when he represented the Queen and inspected graduating officer cadets at the Sovereign‚Äôs Parade at the Royal Military Academy Sandhurst in Camberley, Surrey.
'But on the other hand if you think back to King George V, who had a beard, obviously he was Admiral of the Fleet but he was also a Field Marshall and he often wore Army uniform with a beard.'
Mr Vickers added.'I think if you've retired from the Army you probably do need somebody's permission to wear your old uniform.
'But I think the statement covers all those possibilities.'
Harry's uniform revealed that some time after leaving the Army in 2015 he was promoted to the rank of major, an honour that was bestowed by the Queen.
The prince wore a frockcoat uniform of the Blues and Royals ranked to major, with large gold embroidered crowns.
It is the Queen's prerogative that senior members of the royal family are promoted in line with their peers because they hold royal military appointments.
Harry left the forces in June 2015 and was first spotted with a beard in September the same year.
He had a beard when he wore a military dress coat at the Cenotaph last November, which prompted criticism from some quarters.