The agency says neither Clinton nor Obama received the packages, and neither was at risk of receiving them because of screening procedures.
It says the devices were discovered late Tuesday and early Wednesday.
A U.S. official tells The Associated Press that a "functional explosive device" was found during screening at Bill and Hillary Clintons' suburban New York home.
The official says investigators believe the explosive is linked to one found Monday at the compound of liberal billionaire George Soros.
The Secret Service says a second package was addressed to Obama and was intercepted in Washington.
White House spokeswoman Sarah Huckabee Sanders says in a statement Wednesday: "These terrorizing acts are despicable, and anyone responsible will be held accountable to the fullest extent of the law." She adds: "The United States Secret Service and other law enforcement agencies are investigating and will take all appropriate actions to protect anyone threatened by these cowards."