Virginia's plan for redistricting its 40-member state Senate was rejected yesterday by the Justice Department on the grounds that the proposal discriminates against black voters in Norfolk, the state's largest city.

The action, which came under the 1965 Voting Rights Act, was the first decision by the Reagan administration on any state's plan to reapportion election districts on the basis of the 1980 census.

Virginia's plan for redistricting its 100-member House of Delegates, which also has been challenged by civil rights groups, is under consideration by Justice. A ruling is due Aug. 16, a department spokesman said.

Yesterday's decision, hailed by the state's American Civil Liberties Union chapter as a demonstration of the value of the Voting Rights Act, objected specifically to the way the Virginia legislature divided Norfolk into two single-member state Senate districts.

"The city of Norfolk was divided into two districts in such a way that it split. . . . fragmented the black population and . . . diluted the black vote," the Justice spokesman said, summarizing a three-page letter sent by the department's civil rights division to the state.

According to the spokesman, Justice found that the drawing of the district boundaries failed to meet the Voting Rights Act requirement that any charge in election procedure must be nondiscriminatory. At present, Virginia is one of the states in which all changes to election districts must be reviewed by Justice to ensure fair treatment of minorities.

Voting Act provisions requiring such advance federal clearance of changes in election procedures in Virginia and eight other states, most of them southern, expire next year. Many southern politicians argue that the provisions discriminate against their region.The administration has not decided whether to recommend extension.

Earlier this year, before the legislature adopted the Virginia plan, Richmond Sen. L. Douglas Wilder, the only black in the Senate, contended that the proposed north-south division of Norfolk -- a city whose population is one-third black -- would slice the city's predominantly black neighborhoods in half.

The new plan was designed to replace one in which Norfolk was allocated three senators, who were elected by the entire city. One black member of the House of Delegates called even the north-south division preferable to the at-large scheme in Norfolk, a city of 263,000. Norfolk Del. William Robinson Jr., called the north-south proposal "the lesser of two evils."

Asserting that the choice of boundaries was made "with the full awareness and expectation that it would fragment the black electorate," James P. Turner, acting assistant attorney general in charge of the civil rights division, wrote that the state "has presented no plausible, nonracial justification" for the new lines.

While yesterday's ruling may serve as a signal of administration intentions in the field of civil rights, with Virginia's state Senate elections not scheduled until 1983, it is less likely to have quick impact on electoral patterns there. House of Delegates elections are scheduled for this fall.

Under the law, Virginia can either amend the plan to satisfy Justice scrutiny, or it can challenge the ruling in federal court in Washington.

State Sen. Hunter B. Andrews, chairman of the committee that drew the lines for the new districts, said yesterday his committee will seek a meeting with Justice over the dispute and will attempt to draw new boundaries that would resolve the complaint. He noted that the legislature is due to reconvene in Richmond Wednesday, but said he doubted the issue can be resolved then.

"The same thing happened 10 years ago. We met, made adjustments to the lines which they subsequently approved," said Andrews. He declined to comment on the department's action, which some legislators had warned was likely.

Chan Kendrick, executive director of the state ACLU, said last night, "We're real pleased." Virginia NAACP chief Jack Gravely described his group as "cautiously excited" by the ruling. "It is an initial advancement, but in no way do we view it as a victory," he said.