Prince Frederic von Anhalt says he was awakened at 3 a.m. Sunday and discovered two men in his living room. He says they took off on foot and he pursued them down the block.
The 67-year-old Von Anhalt says he fell while chasing them and injured his hip.
He says windows and a door at his home were damaged, and paintings, statues, computers and camera equipment are missing.
The Los Angeles Police Department confirmed it is investigating a burglary after dispatchers received a call from Gabor's home Sunday morning.
Gabor, a sex symbol of the 1950s and 1960s, made headlines in recent months after a series of hospitalizations. She had most of her right leg amputated in January because of gangrene.