Her comments came as UNHCR marked the halfway-point in a 10-year campaign to end the plight of the millions around the globe deprived of a nationality.
Statelessness leaves people politically and economically marginalised, and particularly vulnerable to exploitation and abuse.
They are often deprived of an education, medical care, the right to marry or even receive a death certificate.
"It is total invisibility," Ms Blanchett said, lamenting that "they experience marginalisation and exclusion from cradle to grave".
At the same time, parents deprived of a nationality often pass on the "desperate and horrific gift" of statelessness to their children, she said, describing it as an "inhumane and heartbreaking and devastating situation".
It was all the more heartbreaking to witness since the problem could be solved.
"It is a man-made problem and it is solvable," she said, pointing out that states "define citizenship and so states do have the power to remove the roadblocks to citizenship for stateless people."
In 2014, UNHCR estimated there were around 10 million stateless people worldwide, but High Commissioner Filippo Grandi told journalists last week that the true numbers were unclear since many such people "are quite invisible".
Mr Grandi told a meeting of UNHCR's Executive Committee Monday that "there have been important achievements" towards the goal of eradicating statelessness by 2024.
Over the past five years, some 220,000 stateless people have acquired a nationality thanks to concerted efforts in a number of countries.
Sierre Leone was praised for its work to remove gender-discrimination from nationality laws and allow mothers to pass on citizenship to their children.
But Mr Grandi cautioned that "progress is far from assured".
"Damaging forms of nationalism, and the manipulation of anti-refugee and migrant sentiment -- these are powerful currents internationally that risk putting progress into reverse," he said in a statement.
Mr Grandi stressed that solutions were urgently needed for millions without citizenship or at risk of becoming stateless, including Myanmar's Rohingya and in India's Assam.
Later Monday, UNHCR's prestigious Nansen Award will be attributed to Kyrgyz human rights lawyer Azizbek Ashurov for helping Kyrgyzstan become the world's first country to end statelessness, working through his organisation Ferghana Valley Lawyers Without Borders (FVLWB).