A German-American Friendship Garden, expected to include one ceremonial oak tree from Germany and assorted flowers, is being planned for the Washington Monument grounds along Constitution Avenue, according to the U.S. Park Service and a group that is promoting the project to help mark the 300th anniversary of German settlement in America.

The design and dimensions of the garden have not yet been set, pending approval by the National Capital Planning Commission and the Fine Arts Commission, but the Park Service has already agreed to donate land for the project, and formal groundbreaking ceremonies for the park are scheduled for Oct. 5.

Neither the Presidential Commission for the German-American Tricentennial nor the Park Service yesterday would disclose the size of the park, which will be located on Constitution Avenue between 15th and 17th streets NW. A Park Service spokesman said the agency hasn't yet received what he said is the latest garden plan, which will be presented to the NCPC and the Fine Arts Commission for approval Oct. 6.

West German President Karl Carstens will be a special guest at the groundbreaking ceremonies and will help plant the oak tree. Landscaping of the garden, which will be open year round, is not expected to start until the spring of 1984.

The garden will cost an estimated $500,000, according to the tricentennial commission, and a special Friendship Garden Fund already has raised more than $100,000 in private donations. Among the contributors are German-American clubs, former World War II GIs, governors and mayors in West Germany, German corporations here and in West Germany, and American companies doing business in West Germany.

"It will serve as a beautiful and enduring symbol of German-American contributions to this country and the lasting friendship between the peoples and governments of the United States and the Federal Republic of Germany," said a statement released by the tricentennial commission.

A Baltimore architectural firm, Oehme, Van Sweden and Associates, has agreed to design and supervise construction of the garden without charge, according to the commission.

Dedication of the garden next month is intended to highlight the climax of tricentennial events that have been going on all year.

Oct. 6 will mark the 300th anniversary of the date 13 Mennonite families from Krefeld landed in Philadelphia in 1683 and founded Germantown.

The 1980 U.S. Census reported that more than 26 percent of the nation's population is of full or partial German descent, making that group second only to those of English origin nationally, the tricentennial commission said.