Speaking about the boycott call, one New York officer said the song would make policing the city much harder.
The song - which prompted the New York City police officers' union on Monday to call for a boycott of Mr Springsteen's concerts - was received with loud cheers and scattered boos.
One heckler had to be removed after he approached the stage, making obscene hand gestures to Springsteen.
The song American skin refers to Amadou Diallo, a 22-year-old immigrant shot 41 times by city police as he stood in the hallway of his apartment block in the Bronx.
The policemen involved - who said they believed Mr Diallo was pulling out a gun when in fact it was his wallet - were acquitted on charges of murder in February.
The shooting was followed by several days of unrest in New York as civil rights activists mounted protests against the killing.
Although the song does not mention Mr Diallo by name, it opens with the words "41 bullets, 41 bullets" and includes the line, "Is this your wallet? Is this your life?"
The song also has the line: "It ain't no secret you can get killed just for living in your American skin."
Boycott
The Patrolmen's Benevolent Association, which represents the city's 27,000 police officers, has called on members to boycott the shows and to refuse working overtime security for the concerts.
Speaking about the boycott call, one New York officer said the song would make policing the city much harder.
PBA's first vice-president John Puglissi said: "This is a time for healing, and this song just reopens old wounds."
Springsteen has not recorded or released the song in any format. Neither has he made any comment about its content or inspiration.
He first performed American Skin in Atlanta last week during a set with his E Street Band.
Mr Diallo's mother has reportedly thanked Springsteen for remembering her son.