The arrest came after authorities Friday responded to two more devices - one in Florida, the other in NY - pushing the total number of packages found by law enforcement to 12.
The FBI, which is leading the investigation into the packages, has only confirmed the existence of 11 packages and has not released any information about suspects or any potential motivation for the mailings.
Investigators are nevertheless treating the devices as "live" explosives, not hoaxes, said James O'Neill, police commissioner of New York City where two of the parcels surfaced.
US President Donald Trump on Friday lashed out at CNN for blaming him for the current spate of bombs being sent to present and former high-ranking officials including his predecessor Barack Obama, saying it is "funny" how he is being criticised by the cable news network and others.
Cesar Sayoc, the man suspected of sending at least a dozen parcel bombs to high-profile critics of President Donald Trump, is a 56-year-old registered Republican in Florida with a lengthy criminal history, according to public records. None had exploded, and it wasn't immediately clear if they were meant to cause physical harm or simply sow fear and anxiety.
Trump and his media allies have pointed to the overheated rhetoric of those on the left, including the hounding of members of the administration as they eat at D.C. restaurants. Soros has called Trump's presidency "dangerous". The U.S. Postal Service searched their facilities 48 hours ago and the most recent packages didn't turn up.
Three more devices were linked to the plot - two addressed to former vice president Joe Biden and one to actor Robert De Niro - bringing the total to 10 as authorities warned there might well be more. The source of the packages is under investigation, and authorities have not said whether there is a motive. The package addressed to Brennan was sent to CNN's NY offices.
Clapper, who has frequently criticized Trump, vowed to CNN Friday morning that he wouldn't be intimidated in light of the discovery.More news: Jordan flood death toll rises to 20, a lot of them school pupils
The packages were sent in manila envelopes with bubble wrap, marked with computer-printed address labels.
One of the packages was recovered at a South Florida office of Rep. He said there was no imminent danger to the Time Warner Center, where CNN's NY office is located.
The bombs have heightened tensions during the closing days of a highly contentious campaign ahead of the November 6 elections in which Democrats are battling to seize control of Congress now held by Trump's Republican Party.
"Stop blaming others. Look in the mirror", Brennan tweeted.
The devices sent to Clinton, De Niro, Obama, the CNN offices and Waters' East Coast office are either with the Federal Bureau of Investigation or headed to the agency's lab in Quantico. Debbie Wasserman Schultz, D-Fla., because her name was listed as the return address on all of them. Just two days earlier, CNN's offices in NY were evacuated when the package for Brennan, addressed to him at the network, was found in the mailroom.
Asked at the same news conference why it appeared that Sayoc allegedly only targeted liberal political figures, Attorney General Jeff Sessions said "he may have been a partisan. appears to be partisan, but that will be determined as the case goes forward". Investigators are homing in on a postal facility in Opa-locka, Florida, where they believe some of the packages originated, another official said.
The bombs are about 6 inches long and packed with powder and broken glass, according to a law enforcement official who viewed X-ray images.
The packages, containing devices that appear to be explosive devices, began to show up on Monday, starting with billionaire George Soros, a major donor to Democrats and Democratic causes.