The news followed the announcement of the discovery of a bomb at the home of Hillary and Bill Clinton in New York earlier on Wednesday.
On Tuesday, an explosive device was found at the New York home of billionaire philanthropist George Soros.
Donald Trump was quickly briefed on the situation and the White House denounced the incidents.
“We condemn the attempted violent attacks recently made against President Obama, President Clinton, Secretary Clinton, and other public figures," said White House press secretary Sarah Huckabee Sanders. She said the sending of the packages was "despicable" and vowed anyone responsible for sending them would be held accountable to full extent of the law.
The New York Times said that the Secret Service - the oldest of the US law enforcement agencies said it “has intercepted two suspicious packages addressed to Secret Service protectees”. These were subsequently identified as Ms. Clinton and Mr Obama.
The device addressed to Mrs. Clinton in Westchester County was found late on Tuesday by a Secret Service technician who screens mail for her office, the statement said. The package addressed to Mr. Obama, who lives in the well-heeled Kalorama neighbourhood of Washington DC and who counts Ivanka Trump and Jared Kushner, was intercepted by Secret Service staff in the capital early on Wednesday.
“The packages were immediately identified during routine mail screening procedures as potential explosive devices and were appropriately handled as such,” the statement said. “The protectees did not receive the packages nor were they at risk of receiving them.”
There was no immediate word on whether either the Clintons or the Obamas were at home when the devices were received.
Sarah Sanders: “We condemn the attempted violent attacks recently made against President Obama, President Clinton, Secretary Clinton, and other public figures...” pic.twitter.com/u3eHsVV1Oy
— Kaitlan Collins (@kaitlancollins) October 24, 2018
The statement said the agency had “initiated a full scope criminal investigation that will leverage all available federal, state, and local resources to determine the source of the packages and identify those responsible.”
The discovery of the packages came after a small bomb was found earlier this week at the home of billionaire liberal donor Mr Soros, in the New York City suburb of Katonah.
An official told the Associated Press that investigators were reviewing surveillance video to determine whether the package had been sent through the mail.
“The components were there for an explosive device,” said the official. “It was not a hoax device.”
The Jewish Mr Soros has also been the target of anti-Semitic smears. Some have falsely accused him of being a Nazi collaborator during World War II, when he was a child in Hungary. Most recently, he has been accused by some elected Republicans of funding the migrant caravan making its way from central America into Mexico, something there is no evidence to suggest is true.
The device sent to Clinton was similar to the one found on Monday at Mr Soros' home, the Times reported, citing a law enforcement official.