Cameron Station, a 166-acre Army base in Alexandria's West End, was included yesterday in a list of 22 military facilities around the country that Defense Secretary Caspar Weinberger said could be closed down to cut Pentagon spending.

"I'm shocked," said Alexandria Vice Mayor Patricia S. Ticer when she heard of the possibility that the 42-year-old base would be closed. "If they sell that property it will have an enormous impact. It's such a huge piece of land, it's a city by itself."

If new homes and shopping centers are built on the largely open tract, Ticer said, Alexandria will face serious street and sewer problems.

Cameron Station is headquarters for the Defense Logistics Agency, the Pentagon's procurement arm, which awarded $15 billion in contracts last fiscal year. The base is operated by 4,300 civilians who work in its eight brick buildings.

Sen Barry Goldwater (R-Ariz.), chairman of the Senate Armed Services Committee, said Weinberger provided the list in response to Goldwater's request for ways to save money. The document says it "should not be considered an official Department of Defense representation," even though it was prepared by the Pentagon.

Goldwater said that the list reflects the view that the facilities "could be closed with little or no adverse effect on our national security." Even so, he predicted that President Reagan would not support the closings because he could not muster enough support in the Congress.

"While my colleagues clamor for additional reductions in the defense budget," said Sen. Goldwater, "they do not want such reductions when they affect programs or facilities located within their states and districts."

The 21 other facilities are:

New Cumberland Army Depot, Pa.; Philadelphia Support Activity, Pa; Fort Wingate Depot Activity, N.M.; Army Material Mechanic Research Center, Mass.; Letterkenny Army Depot, Pa.; Fitzsimons Army Medical Center, Colo., and Fort Ruger, Hawaii.

Also, Fort Devens, Mass.; Jefferson Proving Grounds, Ind.; Naval Air Rework Facility, Alameda, Calif.; Naval Regional Medical Center, Oakland, Calif.; Camp Smith, Hawaii; Naval Air Station, Seattle, and Philadelphia Naval Shipyard, Pa.

Naval Complex, Great Lakes, Ill.; Naval Air Station, South Weymouth, Mass.; Naval Air Development Center, Warminster, Pa.; Chicago Reserve Component at O'Hare Airport, Ill.; W.K. Kellogg Regional Airport, Mich.; Blytheville Air Force Base, Ark.; McConnell Air Force Base, Kan.