The magazine said the person had been treated and was in a stable condition. No further information was immediately available.
"Vaccines do have side effects and allergic reactions - while uncommon - are known to occur. We also know that based on clinical trials and reports of adverse effects in other jurisdictions, reactions such as these are rare but have been reported with the Pfizer vaccine," the NYC Department of Health and Mental Hygiene said in a statement on Wednesday as quoted by Newsweek.
It said the case had become the first of its kind among more than 30,000 people vaccinated in the city.
The United States has authorized two vaccines - produced by Pfizer and Moderna - for an ongoing mass immunization. Each vaccine is administered in two shots with an interval of several weeks required between injections. The Defence Department is in charge of the vaccines’ distribution as part of the Trump administration’s Operation Warp Speed.