The study, published in the Journal of the American Medical Association, said one in every 1,000 newborns was affected in 2009.
The number of pregnant women testing positive for illegal or legal opiates increased fivefold in the same period.
The report says abuse of prescription painkillers is partly to blame.
The study, the first of its kind in the US, was based on records from more than 4,000 hospitals across the country.
It found that in 2009, about 13,500 babies were born with withdrawal symptoms – roughly one every hour.
Not all babies born to women who used opiates during pregnancy showed the symptoms, the report said.
But those that did were often born earlier and smaller, suffered seizures, restlessness, breathing problems or difficulty feeding and often required treatment with the opiate-replacement drug methadone to help wean them off their dependency.
“They appear uncomfortable, sometimes they breathe a little faster. They’re scratching their faces,” said Dr. Stephen Patrick of the University of Michigan, who worked on the study.
The babies were kept in hospital for an average of 16 days, compared to three for health babies.
As most were born to mothers who were entitled to financial help with their medical costs, the study said this was placing a serious burden on health budgets.
The researchers said many pregnant women were legitimately taking pain-relieving opiates on prescription, but warned that more must be done to find ways of protecting unborn babies from powerful drugs.
Dr. Stephen Patrick said the findings were “part of a bigger call to the fact that opiates are becoming a big problem in this country”.
An editorial in the journal accompanying the study said that while such opiate medications provide “superior pain control” they have been “overprescribed, diverted and sold illegally, creating a new opiate addiction pathway and a public health burden for maternal and child health”.
In 2011, the Centers for Disease Control and Prevention (CDC) warned that painkiller abuse in the US had reached “epidemic proportions”.
It said overdoses of pain relievers cause more deaths than heroin and cocaine combined.
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