The second package was addressed to the state transportation department.
According to officials, the two packages were identical and contained a note that said: "Report suspicious activity. Total [expletive]! You have created a self fulfilling prophecy."
Authorities initially said the packages exploded, but later said there were no blasts.
One package was opened at the Jeffrey Building in downtown Annapolis and another one was opened 15 minutes later at the Maryland Department of Transportation building in Hanover.
On Thursday afternoon, officials said a third suspicious package was found at a Baltimore courthouse. It wasn't immediately clear if the package was linked to the first two packages.
The incidents remained under investigation.