The group threatened well-known white nationalists including Richard Spencer, Jason Kessler and David Duke.
Addressing the men directly, the video narrator said: “You are not safe. The blood of Heather is on your hands, and you will pay for it in blood.”
The announcement comes after Heather Heyer, 32, died and more than 30 people were injured following a violent white nationalist rally on Saturday in Charlottesville.
Ms Heyer was killed at the scene when a car rammed into a crowd protesting against the rally.
Andrew Anglin, founder of the neo-Nazi Daily Stormer website, was also threatened by the hacking group.
The narrator said: “If you value your life, Mr Anglin, you will need to flee the country.
“We will find you, we promise.”
The Daily Stormer site has been kicked off GoDaddy and barred from Google.
In the six minute long video, Anonymous also announced that it will focus on taking “down domestic terrorism websites” and sites which share a similar ideology.
The video’s narrator added: “Citizens of the world, we are anonymous, and we are angry.
“Anonymous finds it a sad state of affairs [that in 2017] we still have Nazi party flags flying high and terrorists still killing for the Nazi cause.”
The group also warned the Westboro Baptist Church members against attempting to show up to Heather Heyer’s funeral, saying it would be their last if they do.
Gabriella Coleman, an expert on Anonymous, has said that some of the group’s participants are also in AntiFa and “have no problem punching Nazis”.