A Washington philanthropist and author has persuaded a New York federal judge to hold a special court hearing on the Reagan administration's decision to dismiss the government's 13-year-old antitrust suit against International Business Machines Corp.

U.S. District Judge David N. Edelstein said yesterday that he would hold a hearing on April 8 on a motion by Philip M. Stern to investigate whether the suit was properly dismissed on Jan. 8 when the assistant attorney general in charge of antitrust, William F. Baxter, summarily dropped the suit on the grounds it had no merit.

Among other things, Stern has charged that the suit was improperly dismissed because neither the court nor the public had an opportunity to review the dismissal.

Stern also charged that the dismissal is null and void because Baxter should have been disqualified from participating in the suit because of an earlier business relationship with IBM's lawyers.

"My sole interest . . . is to ensure to the extent practicable that the antitrust laws are vigorously and properly enforced and that the public interest will be served by the ultimate outcome of the IBM case," Stern said in a legal brief.

"After the case had been reviewed by attorneys general and assistant attorneys general, suddenly it is dismissed without merit," Stern said in a telephone interview. "Obviously questions ought to be raised."

Edelstein called for a hearing after Stern's lawyers met with the judge yesterday morning. Having presided over the case's 7-year-trial, Edelstein has criticized the dismissal.

Additionally, Edelstein accused Baxter of a possible conflict of interest by failing to disclose his relationship with IBM to the judge or Congress before the case was dismissed.

However, up until Stern's petition, Edelstein has indicated that under legal procedures, he had relatively little power to review Baxter's actions.