"Art From the Hermitage Museum in Leningrad," the vast Soviet exhibition scheduled to open in Washington in May, has in effect been canceled, two highly placed government officals said yesterday.

The U.S. government has declined to certify that the Russian shows is "in the national interest," and the International Communications Agency will not sign the necessary legal waivers allowing the show to tour here. The decision comes after the show's sponsor, Control Data Corp., the Minneapolis computer firm, reportedly has already spent the largest portion of a $1 million investment, and means that the National Gallery of Art has lost its major summer show.

Officials at the Gallery, the computer firm and the Soviet Embassy here have been waiting for the requisite "waiver of judicial seizure" that must be granted by the I.C.A. in order for the exhibition to proceed. That waiver, which protects Russian state-owned treasures from seizure in U.S. courts, will not be forthcoming, a high governmental official said yesterday.

Without the waivr, a Soviet diplomat said yesterday, "the Ministry of Culture will not send its works of art the the United States."

Although officials at the State Department, the National Security Council and the I.C.A. -- the agency which handles international cultural exchanges -- have ruled against the exhibition, the government decision has not yet been announced. Spokesmen at Control Data and at the Gallery have declined to comment on the matter until they are officially informed that the waiver will not be granted.

The move against the exhibition -- like the threatened boycott of the Olympic Games in Moscow -- is yet another sign of American disapproval of the Soviet invasion of Afghanistan. The 400-item show, which was to spend two years here touring five cities -- Washington, New York, Minneapolis, San Francisco and Detroit -- would have been on view at the foot of Capitol Hill throughout the major protion of the 1980 campaigns.

Unlike previous exhibits sent here from the Hermitage, this one was to survey all the departments of that huge museum. Prehistoric carvings, works of Scythian gold, icons, medals, drawings, prints and paintings were to have been displayed.

Although international art shows have constitencies much smaller than the Olymics, governments, in recent years, have come to regard them as powerfully symbolic.

The Gallery had set aside the large display space needed for the Hermitage exhibit, and contracts for the design and construction of its installation were ready to be signed. But Control Data Corp. will bear the major costs of the cancellation.

The computer firm had planned to print 250,000 copies of the exhibition's catalogue. The illustrated book, with 400 pictures, all of them in color, is ready for the presses, and costly paper for the catalogue has been specially manufactured. Control Data has also spent additional large sums on educational materials, posters, plane trips to Leningrad, press kits and similar expenses. The company also was to have borne the cost of insuring the priceless objects.

Because large art museums plan their major shows some years in advance, the five-city tour of the Hermitage exhibit is not likely to be rescheduled -- even if the Soviets were to begin withdrawing soliders from Afghanistan soon. The show would have been seen here in the National Gallery's East Building. Gallery officials not entirely surprised by the government's decision, already have begun considering replacements for this summer's Russian show.