A hazardous materials response team was called and determined the white powdery substance was harmless.
"They did evacuate for a short time," Jones said. "The substance was determined to be nontoxic, and an investigation is continuing."
Testing is under way to determine exactly what the substance is.
The letter was addressed to "Governor Codey." Codey was New Jersey's acting governor from November 2004 to January 2006.
Jones would not say whether the letter bore a return address. More than 30 similar mailings have been received at governors' offices nationwide since Monday, all postmarked from Texas. The FBI is investigating.
Letters containing anthrax powder killed five people in the fall of 2001. Some were processed at the post office in Hamilton, just outside Trenton, and were addressed to the New York Post and NBC in New York.
Two postal workers at the Hamilton center contracted the skin form of anthrax.
Five other people were infected by anthrax in New Jersey, but none died.