The letter was written just six hours before her execution on 8 February 1587.
The 430-year-old handwritten letter has not been on display in Edinburgh since 2009.
For preservation reasons, the letter was only to be on show for six hours between 10:00 and 16:00. It will now be on show until 19:00. Entry is free.
Queues have started forming at the National Library of Scotland where the letter is on display.
Mary is one of the most fascinating figures in Scottish history.
She became queen of Scotland when she was six days old but spent most of her childhood in France.
On her return her brief reign resulted in disastrous marriages, murder and war.
She gave up the throne at the age of 24 and was a prisoner in England for most of the next 20 years until she executed on the orders of her cousin, Queen Elizabeth I.
Her son James became king of Scotland and England.
Mary's last letter was written at two o'clock in the morning on Wednesday 8 February 1587 as she prepared to meet her death at Fotheringhay Castle in Northamptonshire.
Writing in French to Henri III, King of France - the brother of her first husband - she said: "I am to be executed like a criminal at eight in the morning."
In the letter she said her "crime" was her loyalty to her Catholic faith which, together with her claim to the English throne, made her a considerable threat to her cousin, Elizabeth.
She also expressed concern for the servants she would leave behind who had served her so loyally during her 19-year imprisonment in England.
Towards the end of the letter, she beseeched King Henri to have "prayers offered to God for a queen who has borne the title Most Christian, and who dies a Catholic, stripped of all her possessions".

Police said the tanker, transporting fuel to Nato forces in Afghanistan, was hit by a bomb overnight near the town of Landi Kotal in the Khyber region.
People gathered to collect spilt fuel when another fire broke out, said one senior police official.
At least 14 other Nato tankers were damaged in  a separate attack nearby, at the Torkham border crossing.
The region is a crucial transport route for supplies destined for Nato forces in Afghanistan but the convoys frequently come under attack from militants and criminals.
Local official Shafeerullah Wazir said the tanker was hit by a small bomb in the early hours of the morning.
"The oil tanker caught fire after a blast caused by a small bomb before dawn," the AFP news agency quoted him as saying.
"Villagers from nearby houses rushed and started collecting oil coming out of the destroyed tanker after the fire had been extinguished.
"Suddenly the fire erupted again and at least 15 people including five young boys who had been collecting oil in their buckets were burnt to death."
There were no injuries at the separate attack at Torkham.
No group has claimed responsibility for the attacks, but there has been an increase in Taliban activity since al-Qaeda leader Osama Bin Laden was killed in the Pakistani town of Abbottabad on 2 May.
In the deadliest incident, more than 80 people were killed by a twin suicide bombing targeting police recruits in the north-west.
On Friday, one person was killed and 10 injured when the Taliban attacked a US consulate convoy in Peshawar - the first attack on US interests since US commandos killed Bin Laden.
The Pakistani Taliban said the bombing was to avenge his death.
The last letter of Mary, Queen of Scots, is to be displayed for an extra three hours due to high public demand.
[NEXT_CONCEPT]
A Nato oil tanker has exploded in northwest Pakistan, killing at least 15 people, say officials.