The trio, including two 19-year-olds in New Zealand on a gap-year holiday, have not been heard from since April 16, when they set off on the 7.5-metre (25-foot) yacht Munetra from Bluff, on the southern coast of the South Island.
An intensive aerial search involving two helicopters and an air force P-3 Orion failed to find any trace of the missing vessel and has now been called off, police said.
"Obviously police continue to have very real concerns for the safety of the occupants on the yacht and are working to piece together information about the three occupants on board," inspector Lane Todd said.
He said the missing were Lea Tietz and Veronika Steudler, both aged 19, and the boat's owner Andre Kinzler.
Tietz and Steudler, from Gorlitz in eastern Germany, had both been in New Zealand since September last year and were due to return home next month.
Kinzler, 33, also a German national, had been working on a South island farm for the past four years.
He is believed to have met the teenagers last month and invited them to sail on his yacht.
Todd said there was no evidence of foul play, with police looking at Kinzler's lack of sailing experience as a possible reason for the disappearance.
"We know that he purchased the boat within the past 12 months but the information we've gathered to date suggests his previous sailing experience may have been limited," he said.