The Soviet Union charged tonight that a member of its embassy staff in Grenada was injured Wednesday in a "bandit" attack by American Air Force planes. It lodged a formal complaint with the U.S. Embassy.

A Foreign Ministry note condemned the alleged encroachment on the inviolability of a diplomatic mission and warned that the U.S. government "bears full responsibility for the life and security of Soviet citizens in Grenada."

The protest coincided with a sharp escalation of personal invective directed at President Reagan.

Speaking on the principal national television news program, commentator Genrikh Borovik condemned Reagan's foreign policy as a "brazen" attempt to impose American terms on other nations through military force. He linked Grenada and the Middle East to Reagan's rearmament program and suggested that nothing should be expected from the Geneva arms talks.

"If one is a bandit, liar and murderer in Grenada and Lebanon, he could not be different on the shores of Lake Geneva," Borovik said.

In a rejoinder to the president's televised address last night, the government news agency Tass used extraordinarily strong language to rebutt his "impudent" remarks.

Tass said Reagan had "institutionalized international terror" as policy of his administration and called this "a new, despicable phenomenon" in international relations. It quoted Reagan's explanations as to events that led to the invasion of Grenada and asserted that "there was indeed no word there that wasn't a lie."

Tass also asserted that the invasion was carried out entirely by American troops and that forces sent by Caribbean states "were not even allowed to take part" in the operations, adding, "That rabble was landed in the areas occupied by the U.S. Marines."

Tonight's note to the U.S. Embassy contained the first official demand "for the immediate ending of the aggression against Grenada and the immediate withdrawal from there of all the interventionist forces."

An embassy spokesman said the note was handed to a U.S. diplomat shortly before it was read over the evening television news.

The note said U.S. Air Force planes fired on the Soviet Embassy in St. George's Wednesday. "Having perpetrated a brazen aggression against the independent Grenadan state, the United States made yet another crime by encroaching on the inviolability of a diplomatic mission and directly endangering the life of its staff members.

"The Ministry of Foreign Affairs makes a resolute protest against the bandit actions committed against the Soviet Embassy in Grenada, warns that such action may have serious consequences and again declares that the government of the United States bears full responsibility for the life and security of Soviet citizens in Grenada."

The Associated Press quoted a senior State Department official in Washington as saying the Soviet mission in Grenada has no direct communication with Moscow. He added that U.S. officials had relayed to Moscow reports from Soviet personnel in Grenada about a Soviet national having been "slightly injured in some unexplained way."

It was not clear how many Soviet citizens are currently in Grenada. It is believed that there are about 100, including diplomats and technical personnel.

Tass reported that fighting continued today between U.S. forces and members of "Grenadan revolutionary arms." It said that the Reagan administration was finding itself in international isolation as a result of the invasion, noting that Washington got no support in the U.N. Security Council and was forced to veto a resolution condemning the invasion.

A dispatch from Nicaragua published in the Komsomolsakya Pravda today, however, reflected deeper Soviet anxiety. It said that the Grenada invasion is a prelude to U.S. armed action against Nicaragua.

This new U.S. intervention, the paper said, "is expected in November." It said that the action would be mounted initially by "Somoza forces," helped by the Honduran armed forces. Should this action fail, it said, the armies of Guatemala and El Salvador are due to come to the assistance of the invading force. All of this would be organized and coordinated by the Reagan administration, the dispatch added.