The thief snatched the beige leather shoulder bag by cutting a wire on the case around 7:55 p.m. on Oct. 22, police said.
The unidentified woman was described as about 28 years old, according to a police report.
No arrests have been made.
A Century 21 spokeswoman did not immediately respond to a request for comment.
The department store officially opened to the public earlier this month.
Other notable crimes from the 84th Precinct, which includes Downtown Brooklyn and DUMBO, include:
► A 26-year-old woman was arrested for trying to steal $12 in beauty products and then attacking someone who tried to confront her at Beauty 35 at 523 Fulton St. around 1:10 p.m. on Oct. 25, police said. A manager at Beauty 35 was not immediately available for comment.
► Two unknown burglars stole $300 from cash registers at Bridge Street Cleaners at 204 Livingston St. around 7:30 p.m. on Oct. 27, police said A manager at the dry cleaning business was not immediately available for comment.
► A 49-year-old woman was arrested for stealing $1,700 in clothing from the Macy’s at 422 Fulton St. around 2:56 p.m. on Oct. 28, police said. A representative for Macy’s could not be reached for comment.
► A 68-year-old man was attacked by three men who stole his phone on a northbound F train as it was approaching the York Street station, at Jay and York streets, around 3:15 a.m. on Oct. 29, police said.