Fairfax City police said yesterday they are investigating the apparent burning of a six-foot cross on the lawn of an Hispanic woman who has been active in several ntional minority organizations.

"Nothing like this has happened before," said Marie Agostini, 42, a Health, Education and Welfare Department employe, whose daughter discovered the charred remains of a cross outside her home yesterday morning.

Fairfax City investigators said the incident was reminiscent of cross-burning that occurred "in the same general area" last year. The 6-by-4 foot cross, covered with a white sweater, had been doused with gasoline, police said, "The cross was leaned against a street sign" near Agostini's front door, Det. Sgt. D. E. Kohler said. "We've apprehended no suspects and the case is still under investigation."

Agostini, who has worked in the minority affairs section of HEW since May, said she believes the burning was motivated by her work.

Agostini said she was afriad that the Klu Klux Klan was responsible for the burning, but police said they had found no indication of Klan activity.

"People have told me that some Iranians decided to move out last year after a series of cross-burnings on their lawns," she said, referring to incidents that occurred during the summer of 1978 and were corroborated by police.

"The house was already up for sale," she said, "I just hope nothing happens to it before it is sold."