SAIRR said its recent survey showed that only a third of the country's children lived with their parents and the rest lived with single parents, on their own, with relatives or in foster care.
Just over 39% of children live with their mothers only. About 4% live with their fathers only.
Eight percent of children lived with their grandparents, great aunts or uncles, but without their own parents.
Child-headed households, where the oldest resident is younger than 18 years old, accommodate 0.5% of children.
The remaining 16% of children included those living in care homes and with relatives other than their biological parents, grandparents, aunts and uncles.
‘Kids more likely to have problems’
Thuthukani Ndebele, a researcher at SAIRR said the living arrangements of children could have an impact on their future.
"Those who live without both parents are often more vulnerable to poverty and unemployment, and may also be exposed to various forms of abuse," he said.
Ndebele said SAIRR previous research suggested children who live without both their parents may be more likely to have behavioural problems or even turn to crime.
"Children living with both parents are statistically less likely to become teenage parents or drug and alcohol abusers, and perform better at school," he said.
Apart from burdening the elderly, the absence of parents could also contribute to an increasing state welfare bill, Ndebele said.
"For example, foster care grant beneficiaries increased more than tenfold, from just over 53 000 in 2001 to nearly 600 000 in 2011/12."
In 2011/12, foster care grants cost the government R442m, Ndebele said.