Medical device maker St. Jude Medical
Mr. Starks was detained by airport police on March 16 after a single shell was inadvertently left in an item of his clothing and discovered when he was traveling through the New Delhi airport, a St. Jude spokeswoman said in a statement.
He is fully cooperating with local authorities to resolve the matter.
Starks has been CEO of St. Jude since May 2004.
The company did not say when it expected Starks to be released.
(Reporting by Ben Berkowitz; Editing by Bernard Orr)