Investigators draped the vehicle with a blue tarp and towed it away on a flat bed truck.
The officials weren't authorized to discuss an ongoing investigation and spoke Friday to The Associated Press on condition of anonymity.
The FBI said the packages were "similar in appearance" to other packages they have discovered.
Authorities already were aware at least one Biden package by Wednesday; it had been misaddressed and returned to sender, and postal officials were trying to track it down, two law enforcement sources said.
Friday's arrest came after authorities announced they'd recovered two more suspicious packages. Cory Booker, New Jersey Democrat, and other was addressed to former Director of National Intelligence James Clapper, who is now a CNN commentator.
Bomb squad and canine units joined Federal Bureau of Investigation agents late on Thursday to examine a sprawling United States mail distribution centre at Opa-Locka, northwest of Miami, Miami-Dade County police said.
It was not clear whether Sayoc had been formally charged in the rash of devices addressed in recent days to Democratic figures including former President Barack Obama, former Vice President Joe Biden, Hillary Clinton, California Senator Kamala Harris and Tom Steyer.
The package was apparently not delivered to Mr Biden's home and may have been on its way to being returned to the person listed on the return address of the envelope, the official said.
Attorney General Jeff Sessions said Friday the Justice Department was dedicating every available resource to the investigation "and I can tell you this: We will find the person or persons responsible". "I am confident that this person or people will be brought to justice".
The package to Clapper was addressed to him at CNN's Midtown Manhattan address. But they were uncertain whether the devices were poorly designed or never meant to cause physical harm. "They originated, some of them, from Florida", Homeland Security Secretary Kirstjen Nielsen confirmed during an interview on Fox News Channel.
Breaking: One man in custody in connection with package bombs
Federal authorities have arrested Cesar Sayoc of Florida in connection with the suspected explosive packages discovered this week, law enforcement sources say.
The packages sent to public figures had numerous hallmarks of suspicious mail, including large block lettering and excessive postage aimed at making it harder to track, said Matthew Doherty, who formerly led the U.S. Secret Service's National Threat Assessment Center. Debbie Wasserman Schultz, D-Fla., because her name was listed as the return address on the packages.
The common thread among the bomb targets was obvious: their critical words for Trump and his frequent, harsher criticism in return.
Later on Friday, a 12th package was discovered at a mail sorting facility on the Upper West Side of New York City.
Mr Clapper's was addressed care of CNN.
New York Mayor Bill De Blasio called the suspicious devices an act of terrorism. They said investigators searching for more suspicious parcels had not found any during the previous eight hours. The News Journal said that the Wilmington post office remained open Thursday.
Meanwhile, the Associated Press is reporting a suspicious package was found at a NY post office addressed to former National Director of Intelligence James Clapper.
Authorities are not giving credence to the reports of an image of the ISIS flag on the device, the source said, suggesting they do not believe it's worldwide terrorism.
The packages were sent in manila envelopes lined with bubble wrap, each stamped with six postage stamps bearing the picture of an American flag.
The bombs were taken to an Federal Bureau of Investigation lab in Quantico, Virginia, officials said.
On Friday, shortly before news of the arrest broke, he complained that the packages were slowing momentum for his Republican Party ahead of the November 6 elections, remarks that enraged his opponents.More news: Florida man arrested in connection with pipe bomb packages
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