A Swiss woman who spoke no English was shot and killed in Southwest Washington Saturday night by a man who robbed her and two other members of her tour group as they took an after-dinner stroll near their hotel.

Police speculated that the victim, Mrs. T. Eggimann, about 60, may have been shot because neither she nor the two women with her could understand the robber who took their handbags.

The shooting occurred about 9:30 p.m. in the 900 block of Half Street SW, near the Skyline Inn at South Capitol and I streets SW, where the women and about 50 other members of the group had been staying since arriving here Friday.

The group left Washington yesterday afternoon as police continued efforts to find the robber, who fled immediately after the shooting, dropping one of the three handbags as he climbed a wall and disappeared from view.

Robi Willimann, the tour leader, said he had advised the group to avoid the side streets near the hotel at night.

"I told them not to go on the side . . . " he said.

Willimann described the victim as an active woman of about 60 who had been enjoying the visit to the United States, which began Tuesday in New York.

The victim, who was hit in the upper left chest, died at George Washington University hospital less than an hour after the shooting. She lived in Dornach, a town of about 5,000 people a few miles south of Basel.