Fracking also has been broadly beneficial at the national level too, Greenstone told CNBC.
"The advent of hydraulic fracturing has produced very large benefits for the country" through lower energy prices, he told CNBC. "Those benefits are widely dispersed."
"It is also true that ... hydraulic fracturing has produced lots of benefits on the health side by greatly reducing coal's share of electricity generation," he added.
The U.S. drilling boom, fueled by fracking, has driven down natural gas costs, making the cleaner-burning fuel more competitive with coal. As a result, coal's share of electricity production in the United States has fallen significantly.
The study did not pinpoint the exact cause of low birth weights in areas with fracking operations. The authors said it was potentially due to drilling-related air or water pollution, the chemicals used onsite, increased traffic or another channel.
Greenstone said the authors hope the study will spark new research to identify the exact mechanism for the lower health outcomes among infants, as well as potential impacts on people at other stages of life. That work could lead to a regulatory solution, he said.
"Until we can determine the source of this pollution and contain it, local lawmakers will be forced to continue to make the difficult decision of whether to allow fracking in order to boost their local economies — despite the health implications — or ban it altogether, missing out on the jobs and revenue it would bring," said co-author Katherine Meckel, assistant professor at UCLA.
Several industry groups quickly criticized the study and its methodology following its release.
"This report highlights a legitimate health issue across America that has nothing to do with natural gas and oil operations," the American Petroleum Institute said in a statement.
"It fails to consider important factors like family history, parental health, lifestyle habits, and other environmental factors and ignores the body of scientific research that has gone into child mortality and birthweight."
The authors of the study compared the health of children born to mothers who live near oil and gas wells both before and after fracking operations began. They then compared those results against mothers who did not live near fracking sites.
To further check their work, they compared infants born near wells with their siblings who were not exposed to fracking operations.