The bag belonged to someone who took another flight but whose luggage was on the small private plane that vanished off Venezuela earlier this month.
Vittorio Missoni and his wife were among six people on board the plane.
Curacao is about 320km (200 miles) west of the islands of Los Roques, from where the plane departed for Caracas.
Norman Serphos, a spokesman for Curacao's prosecutor's office, said a German tourist found the bag on Curacao's rocky north coast.
He said the tourist had contacted the owner of the bag, who is in Italy, who in turn called police in Curacao.
Police received the bag on Friday and are working with authorities in Venezuela and Italy, Mr Serphos added.
No other debris from the twin-engine aircraft has so far been found.
Mr Missoni, 58, is the son of the founder of the Missoni brand and co-owned the firm with his siblings.
He was returning from a Christmas and new year holiday with his wife, Maurizia Castiglioni, and two friends - Elda Scalvenzi and Guido Foresti. Two Venezuelan pilots were also on board the BN-2 Islander plane.
Minutes after takeoff, one of the pilots reported that the plane was at 5,000ft and 10 nautical miles from Los Roques airport, Italy's air safety agency has said.
The last radar report showed the aircraft accelerating at 5,400ft before it rapidly lost altitude and speed, veering to the right until it disappeared from the radar.
A ship that specialises in deep-water searches is due to arrive in Venezuela in February to help look for the plane.
A piece of luggage from a missing plane carrying the boss of Italian fashion house Missoni has been found off the Dutch Caribbean island of Curacao.