Barbara Underwood said the charitable foundation had engaged in "unlawful political co-ordination" designed to influence the 2016 election.
The lawsuit seeks to dissolve the foundation, Ms Underwood said.
The foundation denied the charges, calling them politically motivated.
In a statement, Ms Underwood said Mr Trump had illegally instructed the foundation to provide support to his presidential campaign by using the foundation's name and funds it raised to promote the campaign.
The petition also claims that Mr Trump used charitable assets to pay off legal obligations, to promote his own businesses and to purchase personal items.
The attorney general is also seeking to bar the president and three of his adult children, Donald Jr, Eric and Ivanka, from serving on the board of any New York-based charity, "in light of misconduct and total lack of oversight".
The president hit back at the lawsuit on Twitter, saying that "sleazy New York Democrats" were "doing everything they can to sue me". He vowed he would not settle the case.
The lawsuit alleges that the foundation paid $100,000 (£75,000) to settle legal claims against Mr Trump's Mar-A-Lago resort, $158,000 to settle claims against one of his golf clubs, and $10,000 to purchase a painting of Mr Trump to hang at another of his golf clubs.
The purchase of the painting was an example of one of "at least five self-dealing transactions" which violate tax regulations on non-profit charities, the statement said.
"As our investigation reveals, the Trump Foundation was little more than a cheque book for payments from Mr Trump or his businesses to nonprofits, regardless of their purpose of legality," Ms Underwood said. "This is not how private foundations should function."
The Trump Foundation issued a statement denying the charges and accusing the attorney general of holding its $1.7 million in remaining funds "hostage for political gain".