Fiona Hyslop spoke out as MSPs approved a bill that will give Glasgow City Council the power to lend out the artworks, including overseas.
Arts bosses want to display pieces from the collection at venues across the world while its home in Glasgow's Pollok Park undergoes much needed renovation.
It is hoped an international tour of the collection could raise up to £15 million towards the estimated £45 million cost of refurbishments.
But shipping magnate Sir William Burrell, who died in 1958, left his collection of artwork and historical artefacts for the city of Glasgow on the condition that they were not loaned overseas.
Sir William apparently feared the items would be damaged in transit
The Burrell Collection (Lending and Borrowing) (Scotland) (Bill) - which was unanimously approved by Holyrood - changes that, allowing items to be lent out overseas.
Ms Hyslop said the Bill was aimed at "securing the long term sustainability" of the building which houses the collection "while looking at new ways to promote the collection to a wider audience".
She said: "A tour and lending of individual items would bring the collection to the attention of an international audience and enable people from all over the world to see and appreciate it, thus raising its profile and putting Glasgow and Scotland on an international stage."
She added: "We can see from the massive success of the refurbished Scottish National Portrait Gallery, the National Museum of Scotland and, more specifically to Glasgow, the Kelvingrove refurbishment and the new Riverside Transport Museum, what can be achieved by investing in cultural institutions and bringing our museums up to date for the 21st century.
"It results in soaring visitor numbers and increased customer satisfaction. Given its significance, it seems only logical the Burrell Collection should be next."
The legislation has already be scrutinised by a special committee at the Scottish Parliament, which was chaired by Joan McAlpine.
She told Holyrood: "The committee is firm in its belief that the time has come to allow the collection to be seen by a wider audience.
"Indeed I believe we have a duty to the people of Glasgow to promote the collection, which is a hidden treasure, and also a duty to the people of Scotland."
Ms McAlpine said when the collection first went on display in 1983 it had attracted one million visitors a year, but added that visitor numbers had now fallen to less than 250,000 a year.
She said the collection, which includes medieval, Chinese, French and Islamic art, was "still relatively unknown, both here and internationally".
But she added amending Sir William's bequest to allow the artworks and artefacts to go on a "once in a lifetime world tour" would help raise awareness both at home and overseas
She also said the Bill would also require a lending code to be established by Glasgow City Council and the Burrell Trustees, setting out the basis on which the new powers for lending would be exercised.
"The code should safeguard against excessive and over-commercial lending and against very fragile items being put at unreasonable risk," Ms McAlpine said.
Councillor Archie Graham, depute leader of Glasgow City Council and chair of Glasgow Life, said the passing of the legislation "marks the beginning of a new chapter for the Burrell Collection".
He added: "We now have the opportunity to share some of Sir William's outstanding vision with an international audience for the first time.
"Glasgow is Scotland's cultural powerhouse and The Burrell Collection is undoubtedly the jewel in our crown.
"While we take forward proposals to fully refurbish and redisplay the gallery in Pollok Park, we will be able to share some of these treasures with the world and increase the international reputation, not only of Sir William's great gift, but of the city he called home."
Bureell Renaissance will advise on both the refurbishment work and the collection's international tour.
Its chairman Sir Angus Grossart said: "We are delighted with this formal confirmation and with the strong support which we have received in the great challenge which we have set."