Groundbreaking for the Vietnam Veterans Memorial, scheduled to take place next week, has been postponed by Interior Secretary James G. Watt pending approval of changes in the design by both the Commission of Fine Arts and the National Capital Planning Commission.

Watt announced his decision to delay construction in letters mailed on Thursday to the chairmen of each agency. "I am not prepared to act . . . without assurances that the design improvements meet with the approval of the commission," Watt wrote in his letter to J. Carter Brown, chairman of the Fine Arts Commission.

Although the commission has agreed to place the matter on the agenda for its March 9 meeting, the delay could be lengthy because of the nature of the changes in the design agreed to by both critics and supporters of architect Maya Ying Lin's original concept.

Lin's design, which won a juried design competition that attracted more than 1,400 entries and which received the unanimous approval of both commissions, calls for two long walls of black granite engraved with the names of America's Vietnam war dead and set at an angle into the sloping earth of Constitution Gardens near the Lincoln Memorial. Admired by many for its noble simplicity, this design also attracted strong opposition from some veterans and a group of Republican congressmen, who attacked it as "a political statement of shame and dishonor" in a letter last month to President Reagan.

Responding to these critics, representatives of the Vietnam Veterans Memorial Fund, which sponsored the design competition and currently is raising some $6 million for construction, agreed to a compromise early this month which provides that a flagpole and a larger-than-life statue of an American soldier be added to the memorial.

Supporters of the memorial had hoped to have it completed in time to be dedicated on Veterans Day, Nov. 11, but that now seems unlikely. Whether members of the reviewing agencies, whose approval is required by the legislation authorizing the memorial, will regard these changes as "design improvements" is questionable. In its initial letter of approval last July, the Commission of Fine Arts stressed that care should be taken not to alter the basic simplicity of Lin's design.