He left a police station in the city after being ordered to appear in court on 26 November.
This is not 60-year-old Mr Baldwin's first run-in with the law - in 2014, he was arrested for disorderly conduct.
The actor starred in the movie Hunt for Red October and more recently in TV shows 30 Rock and Saturday Night Live.
The alleged altercation occurred in the West Village area of Manhattan on Friday.
Police told US media the actor had claimed his family member had been holding a spot for his Cadillac Escalade SUV when a man driving a Saab station wagon swooped in and took it.
Police say the two men were arguing and pushing each other before Mr Baldwin swung at the 49-year-old man, who was taken to hospital with jaw pain.
After he was charged with misdemeanour assault and harassment, Mr Baldwin denied that he had hit anyone.
"The assertion that I punched anyone over a parking spot is false. I wanted to go on the record stating as much," he tweeted.
US President Donald Trump, whom Mr Baldwin has portrayed on the comedy show Saturday Night Live, said when asked about the arrest: "I wish him luck."
Mr Baldwin has made headlines before for his anger issues.
New York police arrested him in May 2014 after he was caught riding his bicycle the wrong way in traffic and then became belligerent, swearing at the officers.
He was given summonses for the bike violation as well as disorderly conduct.
Mr Baldwin tweeted angrily about the incident, calling New York City "a mismanaged carnival of stupidity" and naming the officer who arrested him.
In 2013, he was suspended from his MSNBC talk show Up Late for using an anti-gay slur when arguing with a photographer in New York City.
The actor later issued an apology, saying he "did not intend to hurt or offend anyone" with his word choice.
Following the incident, his daughter Ireland also defended him on Twitter, saying that "for someone who has battled with anger management issues, my dad has grown tremendously".
Mr Baldwin and his daughter have had a tense relationship in the past.
He apologised publicly in 2007 for calling his then-11-year-old daughter a "rude, thoughtless little pig" in a voicemail after the message went viral online.
In 2011, Mr Baldwin was kicked off a flight after refusing to turn off his phone. The actor said he was playing Words with Friends.
In 1995 he was acquitted of misdemeanour battery charges for punching a photographer in self-defence.
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