The Metro Board selected the Prudential Insurance Co. yesterday to build a $21 million retail and office development on top of the Van Ness-University of District of Columbia Metro station. The station will be the last subway stop on upper Connecticut Avenue when the Red Line is extended in 1981.

Prudential's proposal for joint development of the property Metro owns at the southwest corner of Connecticut and Idaho avenues was the best of six, according to the selection committee that reported to the baord.

Under Metro's joint development concept, the building will go on the tax rolls of the District of Columbia and Metro will receive rent under a 50-year lease that is still being negotiated.

Similar joint development packages have been approved at the Farragut North, Rosslyn and Friendship Heights Metro Stations.

Under the Prudential proposal, five bus bays and 25 drop-off and pick-up parking places will be integrated into the design of the complex and will be ready to use when the Red Line is extended from Dupont Circle-the last stop now-north to Van Ness Center. The entire complex should be ready for occupancy about a year later.

Prudential's plan, designed by Hartman-Cox, includes a tiered effect on the south side of the property so that the view to and from the university buildings is not obstructed.

The structure will contain aboveground walkways and a plaza, with direct connection from the subway to the university, and a shopping-office complex containing restaurants and theaters. The project includes 165,100 square feet of rentable office space and 47,250 square feet of retail space.

Ricahrd Quigley, of Prudential, said that the site offers "attractive potential for Prudential." He noted that the subway line will turn west off Connecticut at the Van Ness station. Thus the station will be a major bus terminal for Connecticut Avenue traffic north of that point.

Jerry A. Moore, Metro board chairman, sought assurances from the staff yesterday that minority contractors or subcontractors would be used on the project. Carl Cannon, Metro's minority development director, said he was seeking 30 percent minority participation.

Quigley, of Prudential, said that "I don't know yet whether that's a problem or not. We will agree to a goal that's attainable." He said 15 percent of the project was already committed to minority firms.