The 28-year-old man, whose name wasn't immediately released, met the woman at the club 1Oak at 453 W. 17th St. and brought her to his home near 11th Avenue and West 42nd Street about 4:30 a.m. on June 4, NYPD officials said.
The two spent some time together and then he fell asleep, prompting her to swipe the jewelry and flee, police said.
The suspect is about 5 feet 6 inches tall and was last seen wearing dark pants, a dark tank top and a gray jacket, police said.
The nature of their relationship wasn't immediately clear.
Anyone with information should contact Crime Stoppers at (800) 577-TIPS (8477).