The Supreme Court yesterday cleared the way for the federal government to deny financial aid to eligible students who have failed to register for the draft.

In a one-paragraph order, the court lifted--at least temporarily--a U.S. District Court injunction that had blocked the government from requiring student loan recipients to certify that they either have registered for the draft or are not eligible for it.

As a result, beginning Friday, as the government had originally scheduled, students eligible for the draft will be required to certify that they have registered for it to qualify for aid for the coming academic year.

The stay, issued without dissent, is no indication of the justices' thinking on the constitutionality of the requirement itself. The government is now appealing the lower court ruling that voided the law. And the Supreme Court, if it accepts that appeal, could not hear arguments on it until next October.

The stay will remain in force until the appeal is resolved.

The ruling is likely to cause confusion on campuses this fall and create the possibility that some students will not get aid simply because they cannot satisfy lenders that they have registered for the draft.

Colleges and students have been left in limbo over the requirement since March 9, when a federal judge in Minnesota issued a preliminary injunction blocking the rule. Because of the injunction, most schools have not been requiring financial aid applicants to fill out the part of the student aid forms that deals with registration.

The lower court judge issued a permanent injunction on June 17, but the court's decision yesterday lifts that.

Students who have filed financial aid applications since March but haven't certified that they have registered, must now do so or forfeit their aid. "This is coming down at a point when it is potentially disruptive to the process," said Dennis Martin of the National Association of Student Aid Administrators. More than half the applications for financial aid for the 1983-84 academic year have already been filed, Martin said.

According to the Education Department, some 4 million students will have to comply with the law by certifying either that they have registered or that they are not required to because they are female or are otherwise ineligible.

The certification process involves checking the appropriate box on the aid application form and signing it.

At the least, all financial aid applications will have to be checked for certification.

Education Department officials yesterday said that they are "delighted" with the court's action but acknowledged that the ruling leaves them somewhat unprepared. "It was difficult for us to know how to proceed," said Richard Hastings, director of the office of student financial assistance. "But we're fully intending to move forward and enforce the law."

Hastings said that his department "would try to minimize the confusion." He said that he doesn't think the court's ruling will cause "chaos" but conceded that "there will be operational considerations at some schools."

The American Civil Liberties Union and the United States Student Association said yesterday that they will work on Capitol Hill to try to delay the requirement.

But Rep. Paul Simon (D-Ill.), the sponsor of a languishing bill that would do that, said, "I don't see any likelihood that either the House or the Senate would pass anything of that kind. And I don't see any likelihood that the president would sign anything."