U.S. Attorney William B. Cummings ordered one of his assistants yesterday not to appear at Arlington political functions as a candidate until the assistant leaves the Justice Department payroll.

Cummings' directive to his assistant Henry E. Hudson, 31, came four days after Hudson appeared at a reception cosponsored by the Arlington Republican Party. According to several of those present, Hudson announced that he would seek GOP backing in what is expected to be a hotly contested race for Arlington prosecutor, a state office.

"[Hudson] definitely said he will be running as an independent and will be seeking Republican endorsement," said Arlington County Board Vice Chairman Walter L. Frankland Jr., one of 300 persons, who attended the GOP reception.

"We all let ourselves be introduced as candidates," agreed Arlington County Board Chairman Dorothy T. Grotos. She and Frankland announced their intention to seek reelection to second four-year terms on the board at the meeting.

"I run a nonpolitical shop," Cummings said yesterday, "and I've told Henry that when he wants to appear as a candidate, I want his letter of resignation. I told him he can attend political functions as an interested citizen but not as a candidate while he's employed in this office."

"I have not announced my candidacy," said Hudson yesterday. He declined to comment on his appearance at the reception, which came as no surprise to many in Arlington. There has been widespread speculation that Hudson, the former chief assistant to Arlington prosecutor William S. Burroughs Jr., would run against his former boss.

If Hudson, a former member of the Arlington Young Democrats, decides to seek GOP endorsement, he would have to resign from his federal post prior to a June Republican mass meeting at which a candidate is to be chosen.

Because of the large number of federal employes in Arlington who are barred by the Hatch Act from partisan political activity, candidates frequently run as independents with major party endorsements.

Last month Burroughs, Arlington's controversial prosecutor since 1974, announced he would seek a second four-year term in a June Democratic primary. John W. Purdy, the senior Democratically endorsed candidate on the County Board, has announced he will challenge Burroughs for the $44,500 per year post.