Justice Gregory Carro in Manhattan announced the decision shortly after Mangione was led into the lower Manhattan courtroom handcuffed and with shackles on his feet, wearing tan prison garb.
In his written decision, the judge said that although there is no doubt that the killing was not ordinary street crime, New York law does not consider something terrorism simply because it was motivated by ideology.
"While the defendant was clearly expressing an animus toward UHC, and the health care industry generally, it does not follow that his goal was to 'intimidate and coerce a civilian population,' and indeed, there was no evidence presented of such a goal," Carro wrote.
Mangione has pleaded not guilty to state and federal charges of killing Thompson, the former chief executive of UnitedHealth Group's insurance unit UnitedHealthcare.
Thompson was shot and killed on December 4 outside a Midtown Manhattan hotel, where the company was gathering for an investor conference.
Last week's killing of conservative activist Charlie Kirk has fuelled fears of a spike in US political violence.
Tyler Robinson, the suspect in Kirk's killing is expected to be formally charged with state crimes in Utah later on Tuesday.
Elected officials from both the Republican and Democratic parties have condemned the killing.
While the killing of Thompson was also widely condemned by public officials across the political spectrum, Mangione has become a folk hero to some who decry steep healthcare costs.
A small group of Mangione supporters gathered outside the lower Manhattan courthouse on Wednesday morning.
One was dressed in a green costume of the Nintendo character Luigi, and another held the red, white and green Italian tricolour with the words "Healthcare is a human right" inscribed on the flag.
About two dozen members of the public - mostly young women - secured a seat in the back of the courtroom to watch the proceeding.
One wore a black T-shirt with the words "Free Luigi" written in white letters.
Trial dates have not yet been set in either the state or federal case.
Mangione has been held in federal custody in Brooklyn since his arrest in December.
with AP
