The family of four saw their protection claims rejected Monday by the city's immigration authorities.
The impoverished Philippine and Sri Lankan refugees helped the former National Security Agency contractor evade authorities in 2013 by hiding him in their cramped homes after he initiated one of the largest data leaks in US history.
They have spent years hoping the Hong Kong government would recognise their cases and save them from being sent back to their home countries where they say they were persecuted.
But the family of four, a mother and her daughter and a single man saw their protection claims rejected Monday by the city's immigration authorities, which said there were "no substantial grounds" for believing they would be at risk if they went home.
They now face deportation.
"These are good people that were driven from their homes by torture, rape, abuse, blackmail and war, circumstances that are really difficult for us to imagine," Snowden said in a video released Thursday.
"Now what they're facing is a transparent injustice from the very people that they asked to protect them," he said.
"Someone in the Hong Kong government has decided that they want to make these families disappear immediately, no matter the cost," Snowden added in the video in which he spoke against a plain white background.
He has been living in exile in Russia since the summer of 2013. Russia's immigration service in January extended Snowden's residency permit to 2020.
After leaving his initial Hong Kong hotel bolthole for fear of being discovered, he went underground, fed and looked after by the refugees for around two weeks.
Their stories only emerged late last year.
The refugees' lawyer, Robert Tibbo has called the decision by Hong Kong authorities "completely unreasonable", and said he had less than two weeks to submit appeals before the families were deported.
He said there was a risk his clients could be detained and their children placed in government custody.
Hong Kong is not a signatory to the UN's refugee convention and does not grant asylum.
However, it is bound by the UN Convention against Torture and Other Cruel, Inhuman or Degrading Treatment or Punishment (UNCAT) and considers claims for protection based on those grounds.
One of the refugees, Vanessa Rodel from the Philippines, who lives in Hong Kong with her five-year-old daughter, broke down over the news of the decision.
Another of the refugees, Ajith Pushpakumara from Sri Lanka, told AFP the government had "taken his whole life".
Lawyers for the Snowden refugees have separately lodged an asylum petition with the Canadian government and are calling for to be expedited.