The lawsuit comes less than a week after press secretary Sarah Huckabee Sanders announced it would suspend Acosta's White House credential, often called a "hard pass," in the wake of the reporter's fiery exchange with Trump at a news conference Wednesday.
Sanders, White House chief of staff John Kelly, deputy communications chief Bill Shine and Secret Service Director Randolph Alles are also included in the suit. The Secret Service officer who yanked Acosta's pass is included as well, though he is not identified by name.
In a statement, Sanders said the lawsuit was "just more grandstanding from CNN," and vowed that the White House will "vigorously defend" itself.
CNN alleges in its legal action, which has been filed in U.S. District Court in Washington, D.C., that Acosta's First and Fifth Amendment rights were being violated with the ban.
Lawyer Ted Olson, who served as Solicitor General under President George W. Bush and who reportedly declined Trump's request to join his personal legal team in March, is one of CNN's attorneys in the suit, a court filing shows.
Acosta, who has frequently clashed with Trump administration officials, had challenged the president about his characterization of a "caravan" of Central American migrants traveling to the U.S.-Mexico border.
A female staffer then attempted to pull the microphone out of Acosta's hand, which he initially refused to surrender. "You are a rude, terrible person," Trump responded as Acosta continued to speak into a microphone being passed around to the gaggle of reporters present for the news conference in the White House.
Later Wednesday, Acosta tweeted that he had been denied entrance to the White House grounds.
Sanders, in a series of tweets the same same day, said the Trump administration will "never tolerate a reporter placing his hands on a young woman just trying to do her job as a White House intern."
Critics and media colleagues quickly pushed back on the statement, arguing that Sanders had mischaracterized the altercation. The press secretary received even more criticism after she tweeted a video of the exchange, which The Washington Post and other outlets said was doctored. That video was first shared by a right-wing commentator associated with conspiracy theory website Infowars, the Post reported.
Later that week, Trump appeared to discard the notion that Acosta had inappropriately placed his hands on the intern — the reason stated by Trump's administration for revoking the pass in the first place.
Acosta "was not nice to that young woman," Trump said in remarks to reporters Friday, but "I don't hold him for that because it wasn't overly, you know, horrible."
CNN is asking the court for a preliminary injunction that would reinstate Acosta's press credentials as soon as possible.
"While the suit is specific to CNN and Acosta, this could have happened to anyone," CNN said in a statement Tuesday morning. "If left unchallenged, the actions of the White House would create a dangerous chilling effect for any journalist who covers our elected officials."
Minutes after the lawsuit was reported Tuesday morning, White House Correspondents' Association President Olivier Knox offered a statement of support for the media outlet.
"Revoking access to the White House complex amounted to disproportionate reaction to the events of last Wednesday. We continue to urge the Administration to reverse course and fully reinstate CNN's correspondent," Knox said.
He added: "The President of the United States should not be in the business of arbitrarily picking the men and women who cover him."
The president has regularly slammed numerous mainstream media outlets "fake news" for their coverage of him and his administration, including The New York Times, NBC News, The Washington Post and others.
Trump has repeatedly singled out CNN in his attacks. And days after CNN's New York offices were targeted with mail bombs allegedly by Trump fanatic Cesar Sayoc, the president said "the Fake News Media" was "the true Enemy of the People."
Acosta has also been the target of criticism for his style in front of the news cameras. Writer Todd Purdum argued in The Atlantic in August that Acosta's "performance journalism" provides the Trump administration with "another convenient villain" in the press.