Authorities said there were no distress calls broadcast from the vessel, no locator beacons were activated and it was not clear what communication devices were on board or whether lifejackets were being used.
Last night police said searchers had found a trail of debris on the tide line and had located fish bins and pieces of wood on the surface.
The search will continue today and, depending on weather and tidal conditions, the police dive squad may be used to locate the wreckage.
It is the third fishing trip that has turned to disaster in the lower South Island this year. In January two died when a recreational boat carrying five people capsized in Foveaux Strait.
A month later only one person survived when a boat with nine members of an extended family on their annual mutton-birding trip capsized in the strait when a rogue wave hit them.
Police said the pair on board The Governor were both Greymouthlocals and were heading towardsthe dock at Milford Sound.
"At the time of the incident there was an easterly wind and also a large amount of fresh water coming in from the sound due to the heavy rain the area had been subjected to [recently]," said Senior Sergeant Cynthia Fairly.
"Helicopters were dispatched to the area [on Saturday night], but by about 8.40pm the weather had closed in and the search was postponed."
The search continued yesterday, joined by several local fishing vessels and a float plane. The weather was fine and clear and the search was extended to the shoreline area.
A Maritime NZ spokeswoman said preliminary inquiries were under way but it was too early to speculate on what might have gone wrong. It was a timely reminder for boaties to ensure they carried the right safety equipment, including two types of waterproof communication devices.
Water tragedies
January
A recreational boat capsized near White Island in Foveaux Strait with five people on board. All five were thrown into the water and two died. The others were spotted in the water by Rewai Karetai, who went and rescued the group.
March
Mr Karetai and seven others were killed when a rogue wave caused his fishing boat Easy Rider to capsize in Foveaux Strait. One man survived and was rescued after 18 hours in the water.