The drug has been approved to treat cough symptoms but only in patients older than 10.
Younger kids could suffer serious side effects or even die if they take the medication.
Tessalon is the main brand under which the drug benzonatate is sold.
Generic versions are also on the market.
The FDA says that from 1982 through May of this year, there have been seven cases where children younger than 10 accidentally ingested benzonatate. Five of those children died.
The Associated Press contributed to this report.