Syria's war has also forced hundreds of thousands of people to seek refuge in Europe, including women who have given birth while trying to move across borders.
The agency said that in the 20 countries hosting the largest stateless populations, "at least 70,000 stateless children are born each year" -- or one about every 10 minutes.
"In the short time that children get to be children, statelessness can set in stone grave problems that will haunt them throughout their childhoods and sentence them to a life of discrimination, frustration and despair," Guterres said.
"Several million children are watching their childhoods slip away without the sense of belonging and protection that comes with a nationality," the report said.
The report notes that in 30 countries national documentation is required to access basic medical treatment, while in 20 countries stateless children cannot even be vaccinated.
The UN agency proposed several measures to eliminate the scourge of statelessness, including the reform of discriminatory laws that prevent mothers from passing on nationality to their children.
Children should also automatically become nationals of the country where they are born, UNHCR further said.
The report identified discrimination as the main cause of statelessness, pointing to 20 countries where nationality can be denied on the basis of ethnicity, race or religion.
In some countries, laws prohibiting such discrimination are ignored in practice, such as the Dominican Republic where people of Haitian descent have often been denied Dominican citizenship, UNHCR said.
The refugee agency has previously set a goal to eliminate statelessness by 2024.