The U.S. attorney's office says Carmine Mandarano surrendered Thursday to Drug Enforcement Agency agents.
He was awaiting a court appearance on charges of illegally distributing controlled substances.
His attorney did not immediately return a telephone message for comment.
A complaint alleges the 61-year-old Mandarano prescribed more than 300,000 oxycodone pills between 2010 and 2012.
The court papers noted that is an extremely high number for someone who specializes in care for asthma, allergies, immunology and smoking cessation.
Authorities say Mandarano's office is in East Islip.
The arrest is the latest in an ongoing crackdown on doctors accused of illegal painkiller distribution.