Henry E. Hudson, U.S. attorney for the Eastern District of Virginia, will not be reappointed to a second four-year term but will continue in office for several months until his successor is selected, a spokesman for Sen. John W. Warner (R-Va.) said yesterday.

"I have not asked to be reappointed and I do not plan to stay on for four more years," said Hudson, whose term expired this month. "I will stay on to finish up some investigations that are underway, and I probably will leave some time in 1991."

Hudson is the chief federal prosecutor for Virginia's rapidly growing urban corridor and oversees 54 lawyers in Alexandria, Richmond and Norfolk.

He is best known for initiating a widespread investigation into corruption in the defense contracting industry and for heading a controversial task force on pornography appointed by former attorney general Edwin Meese III.

The president appoints U.S. attorneys who customarily are recommended by senators of his party and are from the state they will serve in.

The initial candidates to succeed Hudson will be selected by Warner, the only Republican senator from Virginia.

Then Sen. Paul S. Trible recommended Hudson and President Reagan appointed him.

A spokesman for Warner, Phil Smith, said yesterday that a decision regarding Hudson's successor is not expected soon. Warner is interviewing candidates for the job of U.S. attorney in Western Virginia, Smith said, and is not likely to turn to Hudson's job until the other position has been filled.

"Sen. Warner thinks {Hudson} has done a very credible job," Smith said. "Henry Hudson will continue to serve until his successor is chosen."