Daniels, whose real name is Stephanie Clifford, lodged the complaint with the US District Court for the Southern District of New York.
In the suit, Clifford said that Trump made "false and defamatory" statements about her in an April 18 tweet.
Trump's tweet was in response to the release by Clifford the previous day of a sketch of a man whom she claimed warned her in 2011 to "leave Trump alone."
Clifford claimed she was threatened in a Las Vegas parking lot after agreeing to an interview with "In Touch" magazine about her alleged affair with Trump.
After Clifford released a drawing of the man she said threatened her, Trump tweeted: "A sketch years later about a nonexistent man. A total con job, playing the Fake News Media for Fools (but they know it)!" "Mr Trump's statement falsely attacks the veracity of Ms Clifford's account of the threatening incident that took place in 2011," the lawsuit said.
A sketch years later about a nonexistent man. A total con job, playing the Fake News Media for Fools (but they know it)! https://t.co/9Is7mHBFda— Donald J. Trump (@realDonaldTrump) April 18, 2018
"Mr Trump's statement is false and defamatory," it said. "Mr Trump used his national and international audience of millions of people to make a false factual statement to denigrate and attack Ms Clifford.
"Ms Clifford has suffered damage as a result of Mr Trump's false and defamatory statement in an amount to be proven at trial but in excess of $75,000," it said.
Since Trump's statement, Clifford has received further threats and has had to hire bodyguards, the complaint said.
"Ms Clifford has been exposed to death threats and other threats of physical violence, causing her both emotional and economic damages," it said.
Trump has denied having an affair with Clifford but acknowledged last week that his personal lawyer and fixer, Michael Cohen, represented him in negotiations with the porn star.
Cohen has admitted paying $130,000 to Clifford -- a payment the porn star says was made to keep her quiet just days before the November 2016 presidential vote.
Clifford has sued Trump in Los Angeles seeking to have the "hush agreement" invalidated. The next hearing, in that case, has been set for July 27.