State officials initially said the packages exploded, but later said there were no blasts.
Maryland state police spokesman Greg Shipley said mailrooms at state offices across Maryland were being quarantined until it could be determined if any other packages had been sent.
One package was opened Thursday afternoon at the Jeffrey Building on Francis Street in downtown Annapolis and another at the Maryland Department of Transportation building in Hanover.
Shipley said the packages were small, about the size of a book.
“In both instances when the small packages were opened, there was a dissemination of smoke and a smell, that’s the best description we have right now,” he said.
Phil McGowan, a spokesman for the Annapolis mayor, said fire units were called to the mailroom of the Jeffrey Building after an employee there was injured.
The FBI’s joint terrorism task force was assisting in the investigation, the state police spokesman said, adding that the state fire marshal and a number of other law enforcement agencies also responded to the two scenes.
A Homeland Security Department official said the department was aware of the incidents and monitoring them.
New Jersey state police also said they had notified agencies across the Garden State about what had happened, saying it was part of normal protocol when such incidents occur. The New Jersey agencies were advised to be “extra vigilant” in handling mail and packages.