A U.S. judge in Alexandria yesterday ruled that the East German government must pay Arlington County more than $28,000 in black property taxes for an apartment building in which it houses its diplomatic staff.

The ruling by U.S. District Court Judge Albert V. Bryan Jr. is believed to be the first to require such a tax payment under the Foreign Sovereign Immunities Act of 1976, according to attorneys in the case.

The judge's order included $24,000 in real estate taxes for 1977, the first year the Germans owned the building, plus $2,400 in delinquent penalties and $2,100 in interest.

The East Germans, who have fought the taxes on their building, Windsor Park Towers, 1515 S. Arlington Ridge Rd., as well as the court's authority to hear the case, said yesterday through an attorney that they would not pay the tax.

"My client feels this is a political matter and it should be resolved through the State Department," said the lawyer, Stanley Faulkner, who added that he did not know if Bryan's decision would be appealed.

During yesterday's 10-minute trial and in pretrial hearings Faulkner was restricted by his East German clients from cross-examining witnesses and presenting evidence.

Charles F. Flinn, assistant county attorney, said yesterday that the county hopes the Germans will pay and said the county will "wait and see" if yesterday's decision is appealed before trying to enforce it.