Video posted online by the outlet shows the white supremacist speaking to Washington bureau chief Zoe Daniel when he was interrupted by individuals off camera.
Spencer was answering questions on whether he was a neo-Nazi. He said he was not, and was then asked what the "Pepe the Frog" pin he was wearing signified.
"Pepe the Frog" is an internet meme so often used by racists and anti-Semites it was designated a hate symbol
by the Anti-Defamation League.
As Spencer was speaking, a masked individual ran up, socked him in the face and fled. Spencer left, later tweeting there was, "no serious damage."
"It was absolutely terrible," Spencer told CNN's Sara Ganim by phone hours after the assault. "I've certain never had this happen before -- a sucker punch in broad daylight."
D.C. police said there is no open investigation into the assault as Spencer has not filed a police report. Spencer says he called 911 at the scene and plans to file a police report. "I kind of like getting into vigorous back and forth with people who disagree with me," said Spencer. "But punching like that just crosses a line -- totally unacceptable."
He went onto say he feared future targeting, "Certainly, some people think I'm not a human being and I can just be attacked at will."
In November, the racism and anti-Semitism of the alt-right movement were on display in Washington when its members gathered to celebrate Trump's victory.
Atlantic magazine, which is recording footage of Spencer for a documentary, published a video of the same event showing audience members apparently giving the Nazi salute.
"Hail Trump! Hail our people! Hail victory!" Spencer declared.
His remarks then were filled with racist imagery -- including references to "the black political machines" and Latino housekeepers -- as he bashed Democratic nominee Hillary Clinton's minority supporters.
Speaking to CNN on Wednesday, Spencer said his support for Trump had waned
"I am getting worried that he won't work on really big important issues like immigration," Spencer said. "That he'll get caught up on little things like making fun of people on Twitter."
Spencer denied being a white supremacist in a December 2016 interview with Ganim
. But, in that interview he said, "Only white people can support what we call Western civilization." He also has said there should be a "peaceful ethnic cleansing," meaning individuals not of European descent should voluntarily leave the United States.