A high-ranking Alexandria official, indicted last month for allegedly embezzling city funds, has been fired for reputedly falsifying information on two city job applications.

Judith J. Greene, who was on administrative leave without pay pending outcome of her trial, was fired by City Manager Douglas Harmon last week for what he said yesterday was "a violation of administrative procedures."

According to a letter from the city's personnel director, the violation involves references to a master's degree that Greene claimed in two job applications to have received from the University of Virginia. University officials confirmed that Greene had attended the university's Falls Church branch in 1969 but could find no record of a degree, city officials said.

Until last month, Greene, 37, earned $36,400 a year as supervisor of Alexandria consumer affairs. She is the daughter-in-law of Councilman Nelson Greene, and was one of the highest ranking blacks in Alexandria's city government.

Greene's lawyer, David Rosenfeld, said yesterday his client had not been fired, but rather had decided to quit before she received a letter asking for clarification of her job application claims.

"She resigned because she got another job," Rosenfeld said. "She has two children . . . she couldn't go on without any income forever."

City Manager Harmon and Alexandria Mayor Charles Beatley said that Greene has had ample opportunities to challenge the facts or provide clarification of the issue that led to her discharge.

In January, Greene was indicted by a city grand jury and charged with embezzling more than $2,000 in federal funds during early 1980, while she was the city's director of the Office of Human Rights. Rosenfeld said that his client will enter a plea of innocent to the charge.