He was rushed to Staten Island University Hospital North, where he was pronounced dead.
Cali is the first mob boss to be murdered in NY since Gotti ordered the infamous hit on Gambino boss Paul Castellano, having him gunned down in front of Sparks Steak House in Manhattan in December 1985.
The Gambino crime boss was assassinated outside Manhattan's Sparks Steakhouse in a 1985 hit orchestrated by an ambitious capo - John Gotti, Adams reported.
"There are no arrests and the investigation is ongoing", police said.
Cali's body was found in an area of Staten Island that has been home to some of New York's most notorious mobsters and their families.
The driver then reportedly bent down and picked up a license plate that had detached in the crash and handed it to Cali before producing a gun and shooting Cali multiple times. No immediate arrests were made. The New York Post reported that Cali had increased the Gambino family's involvement in drug trafficking, particularly in opioids.
The Gambino Family was once among the most powerful criminal organizations in the USA, but federal prosecutions in the 1980s and 1990s sent its top leaders - including the Gotti brothers - to prison and diminished its reach.
"We thought those days were over", the city's mayor Bill de Blasio told journalists. Gotti then took control of the family. "But I guess old habits die hard".
"Frank Cali was a pretty likeable guy, and also this is not a way the mob would kill one of their own", he said.
Cali's murder recalled the last major last mob hit in New York City more than three decades ago.
A paparazzi darling who sported flashy suits with his signature slick pompadour, police ultimately toppled Gotti and incarcerated him for conspiracy and murder in 1992.
Since 73-year-old Gene Gotti's release in September, after a 29-year sentence for dealing heroin, law enforcement sources have been concerned about the possibility of a bloody power struggle within the family, reports have said. After Gotti went to prison, Cali eventually took over the organization.