Police said Gonzales has been arrested on murder and other charges.
The freakish incident occurred Thursday evening in the Bronx as two emergency medical technicians were responding to a call and a passing motorist alerted them that a man was riding on their rear bumper.
The 25-year-old suspect is in custody but police haven't identified him. Arroyo's partner was injured as she struggled with the man inside the ambulance before the man allegedly reversed the vehicle, running over Arroyo and killing her, according to police.
Mother-of-five Yadira Arroyo, 44, was responding to a call on Thursday night when she and her colleague realised a man was riding on the back bumper of their ambulance.
Arroyo was a 14-year veteran of the FDNY, the mayor said.
He praised the bystanders who helped, naming MTA Police Officer Daniel McDade, who happened to see the tragedy unfold and subdued Gonzalez.
During the press conference at Jacobi, de Blasio said EMTs "do crucial work-they save lives-but they should not ever have to be subjected to violence". Arroyo and her partner pulled over, Arroyo came out and left the door open.
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Daniel A. Nigro, the fire department commissioner, said that she was the eighth member of the NY emergency medical services and only the third female employee to be killed in the line of duty.
Authorities say the EMT had stopped her ambulance in the Bronx at around 7 p.m. Thursday after being told someone was being robbed.
"They were acting very bravely", Nigro said. The man threw the ambulance into reverse, officials said, injuring the second EMT.
Friends, colleagues, community members and even the borough president attended a memorial ceremony Friday at the FDNY station house of an EMT killed in the line of duty earlier this week.
Gonzalez told News 12 that he is innocent.
On Twitter late Thursday, Gov. Andrew Cuomo said "tonight's tragedy in the Bronx is terrible".
"It's a sad night for everybody in the department", Nigro said. "My deepest sympathies to the family".