That compares to just 10% of households being private renters a decade ago.
The survey also indicates a sharp decline in the proportion of households buying with a mortgage.
The details are contained in the Family Resources Survey, which covers about 2,000 households.
The survey suggests that 21% of households are private renters, 14% are social renters, 29% have a mortgage and 39% own outright.
The rise in private renting has been particularly sharp in younger age groups.
In 2004, just 16% of people aged between 25 and 34 were private renters, but by 2014 that had jumped to 47%.
There has been a corresponding fall in the proportion of 25 to 34-year-olds buying a home with a mortgage, down from 66% to 35%.
Nicola McCrudden, the Chartered Institute of Housing's director for Northern Ireland, said the growth in renting was partially explained by not enough houses being built.
"More would-be homeowners and social tenants are being squeezed into renting privately, which could push rents up, causing further housing stress," she said.
"This is unlikely to change unless we build more homes and people can access an affordable mortgage."
More than 20% of Northern Ireland households now live in private rented accommodation, an official survey has suggested.