The ASD rate was far higher than that in the general population, which experts estimate to be somewhere between one and nine cases per 1,000 children, depending on how strictly the disorders are defined.
ASD refers to a group of developmental disorders that hinder people's ability to communicate and build relationships. The conditions range from severe cases of "classic" autism to Asperger's syndrome - a disorder in which a person has normal intelligence and verbal skills, but difficulty socializing and understanding subtler forms of communication, like body language and vocal tone.
Some past research has indicated that children born prematurely have a higher prevalence of ASDs, but the extent of the risk linked to extreme prematurity has not been clear.
This latest study shows not only a substantially heightened risk among children born very pre-term, but also points to which of these children are most likely to be affected.
"The study shows an increased frequency of ASD, but it is mainly among children with other disabilities, such that the risk of it developing in children with no other problems is very low," explained Dr. Neil Marlow, a professor of neonatal medicine at University College London, in the UK, and one of the principle researchers on the study.
For example, 56 of the children in the extremely pre-term group had no impairments in thinking and learning when the researchers assessed them at the age of 6. None of those children met the criteria for an ASD diagnosis at age 11.
In contrast, of the 34 children with moderate to severe cognitive impairment at age 6, six - or nearly 18 % - were diagnosed with an ASD at age 11. Of the 65 children with mild impairment, 6 % were later diagnosed with an ASD.
Most of the children with ASD were diagnosed with classic autism, while three were diagnosed with what is known as pervasive developmental disorder "not otherwise specified" - where children have some, though not all, of the characteristics of autism. None of the children had the milder Asperger's disorder.
Marlow and his colleagues report the findings in the Journal of Pediatrics.
Medical advances have meant that more and more very premature and low-birth weight newborns are surviving. Still, they face increased risks of delayed development, learning disabilities and behavioural problems later on.
"We know that very pre-term babies' brains develop differently to those of full-term babies after birth, and that this is associated with a high frequency of cognitive problems in childhood," Marlow told Reuters Health in an email.
The impaired brain development in these children may account for the high ASD risk, the researchers speculate. And that, they say, means that autism may arise via different mechanisms in extremely pre-term children compared with those who were born full-term - for whom, Marlow noted, genetics are believed to be key.
For parents of children born extremely pre-term, the findings mean that they should be aware of the possibility that their child's learning or behavioural issues could be indicative of an ASD.
"Where a parent is worried about learning or behavioural problems in their very premature baby," Marlow said, "they should seek advice from a professional to see what the nature of these problems is."
The current findings are based on a group of UK and Irish children born in 1995. Marlow said he and his colleagues are currently following a group born in 2006, which may show whether advances in medical care of extremely pre-term children has made a difference in their long-term risk of ASDs.