The lawsuit, filed in federal court on Thursday, is intended to "address the significant constitutional issues at stake,” Jay Sekulow, Trump's attorney, said in a statement.
A federal court judge approved the stay of enforcement of the subpoenas later that day, at the agreement of both parties.
Officials confirmed Monday that the district attorney had subpoenaed Mazars USA, the accounting firm used by Trump and the Trump Organization, for eight years of tax returns for the president and the business.
"Because the Mazars subpoena attempts to criminally investigate a sitting president, it is unconstitutional," court papers argue. "This court should declare it invalid and enjoin its enforcement until the president is no longer in office."
In response to an inquiry regarding the suit, a spokesperson for the company referred reporters to Monday's statement.
“Mazars USA will respect the legal process and fully comply with its legal obligations. We believe strongly in the ethical and professional rules and regulations that govern our industry, our work and our client interactions. As a matter of firm policy and professional rules, we do not comment on the work we conduct for our clients.”
In a statement to FOX Business, Vance's director of communications Danny Frost said the office had received the complaint and would respond "as appropriate in court."
Fox News's Marta Dhanis and Chief White House Correspondent John Roberts contributed to this report.