Theodore M. Gardner, a 16-year veteran agent of the FBI, has been appointed the new chief of the bureau's Washington field office.

Gardner, who had been in charge of the FBI's Minneapolis office, will now direct the nearly 400 agents in Washington, the third largest field office of the FBI. Only the New York and Los Angeles offices are bigger.

He succeeds C. Roy McKinnon, who announced plans to retire effective Nov. 12, after being promoted recently to an assistant director's position at FBI national headquarters here, according to a bureau spokesman. McKinnon, 52, a 26-year FBI veteran, served in several FBI offices throughout the country and was special agent in charge of the San Francisco office before coming to Washington in April 1979.

Garner, a 41-year old former marine, joined the FBI in 1964 after graduating from San Diego State Collge. Born in chicago, he has also served in the New Orleans, San Antonio and Los Angeles FBI offices. For four years in the mid-1970s, Gardner worked at FBI headquarters as a supervisor in the criminal investigative division and later as an inspector.

The Washington FBI field office is perhaps the busiest and politically most sensitive in the country. In addition to investigating robberies of federally insured banks and other routine federal crimes, it has spearheaded several large-scale corruption and fraud investigations in recent years. The office also assigns a major portion of its agents to counter-intelligence work because of the large diplomatic and foreign population here.