Barbara Underwood said on Thursday that 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, Underwood said 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 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 lawsuit alleges that the foundation paid $100,000 (£75,000) to settle legal claims against 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 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," Underwood said. "This is not how private foundations should function."
Schneiderman resigned last month after several former girlfriends accused him of physical abuse.
New York is also seeking $2.8 million of restitution, a 10-year ban on Trump serving as a director of a non-profit in the state, and similar one-year bans for his children Donald Jr, Eric, and Ivanka, who serve on the foundation's board.
Eric Trump distanced himself from his own charitable foundation after the election, the New York Times reported, after it came under investigation by the attorney general for allegedly shifting its resources to the Trump Organization.
The Trump Foundation lawsuit adds to Trump's legal challenges, which include a wide-ranging special counsel investigation into alleged ties between the Trump campaign and Russia. Special Counsel Robert Mueller has indicted several of Trump's associates and raided the home and office of the president's long-time lawyer and fixer, Michael Cohen.
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