The Federal Trade Commission, in an apparently unprecedented action, has asked for an independent probe of the controversial circumstances surrounding the award of a $72,000 contract to Harry Hinkes, the law judge who heard the FTC's antitrust case against the cereal industry.

The commission ordered the inquiry last week "under the supervision of an administrative law judge from outside the agency."

The order was signed by FTC members David Clanton, Paul Dixon and Patricia Bailey. Commissioner Robert Pitofsky and FTC Chairman Michael Pertshuk have removed themselves from the matter.

"We believe that an additional inquiry is in order further to explore the actions officials of the Bureau of Competition took prior to Sept. 7, 1978, with respect to the contract," the three FTC members wrote. On Sept. 7 Hinkes publicly announced his retirement and the general details of the new contract.

Although the commission asked the parties to suggest the timetable and mechanism for the probe, FTC officials said the decision is the first time in the 65-year history of the FTC that an independent prober has been asked to handle an FTC internal investigation. "There is still information that needs to be cleared up," Bailey said.

Announcement of the action comes at a critical time in the debate about the future of the FTC's antitrust arm, the Bureau of Competition, and in the cereal case. The Reagan administration has ordered a three-year phaseout of the bureau's activities; President Reagan was sharply critical of the cereal case during a November campaign appearance in Michigan, home base of the industry's leading companies.

The inquiry has stemmed from charges that the commission staff and possibly Pertschuk acted improperly in approving a $72,000 contract for Hinkes after Hinkes announced his intention to retire. By the end of the year, Hinkes was declared "unavailable" to hear the case.

Hinkes has presided over the case for four years. In order to retain; Hinkes in the case and thus avoid a costly retrial, the commission, in an agreement signed by Petshuk, offered him a contract worth $72,000 a year.

Members of both houses of Congress have raised questions about the contract decision, and some have asked the FTC to bring in an independent law judge to study the matter. Further, cereal company representatives have cited the transaction continually in FTC and federal court proceedings.

Sen. Carl Levin (D-Mich.), who has sought an independent look at the Hinkes matter, said yesterday that the decision "solves some of the problems, but not all of them.

"It's about time they had an independent person looking at this. It's overdue," Levin said. "But the commission still has a lot of power. . . . I will urge the FTC to have an inquiry which is not hobbled by barriers of the scope of the investigation."

But a federal judge this week refused a motion by Kellogg Co., one of the targets of the FTC action, in which the company claimed it was denied due process in light of the commission's handling of the matter. The judge, citing "serious questions of statutory and constitutional violations" raised by Kellogg, said the court has no jurisdiction while the case is in the FTC's hands.

The cereal case was brought in 1972.It charges Kellogg, General Mills Inc. and General Foods Corp. with monopolizing the ready-to-eat-cereal industry through a variety of practices that allegedly raised cereal prices by more than $1 billion during the early 1970s.

The case is novel because it is a test of the controversial shared-monopoly theory which holds that, in an industry dominated by a few companies, those firms can restrict competition by pricing and other alleged monopoly practices.