Update 6.20pm: A boat carrying about 70 suspected asylum seekers has arrived at Geraldton.
The vessel arrived just before 1pm.
The group are now destined for Christmas Island, according to statement from the immigration department.
Immigration officials will make arrangements “as soon as possible” for their transfer to the island’s detention facilities.
Two local men testing a motor in a runabout came across the vessel about 500m offshore.
The vessel was so close to shore the asylum seekers could have swam to store according to a cafe owner.
The boat had a flag that appeared to be asking for help and made reference to New Zealand.
It is understood those on the boat said they had been sailing for 44 days and that they were Sri Lankan.
There are men and women, including children and about four babies, on board. There is also a pregnant woman on board.
A pilot boat has towed the vessel into the port and it is tied up. The passengers remain on the boat.
Premier Colin Barnett said the arrival was a "a serious, unprecedented and unacceptable breach of Australia’s border security".
"I am alarmed that a boat carrying 66 asylum seekers can sail undetected into the Port of Geraldton," the Premier said in a statement.
"The State Government is working cooperatively with the Commonwealth on this issue and will ensure people’s welfare is being looked after.
"Nevertheless, this is a serious, unprecedented and unacceptable breach of Australia’s border security.
"That a boat, laden with people, can sail into a busy regional port in broad daylight is shocking."
One witness told The West Australian: "It's full of boat people. It was drifting out there, right in front of Dome."
It is understood a temporary processing centre has been set up at the port.
In a statement Customs and Border Protection Services said it was "responding to a suspected irregular entry vessel which arrived within the harbour limits of Geraldton this afternoon.
"Initial indications suggest there are 66 people on board.
"Customs and Border Protection officers and Western Australian Police are responding to the arrival."
Owner of the Dome Cafe, Graham Sertorio, told The West Australian: "It wasn't a cray boat. It's full of boat people.
"It was drifting out there, right in front of Dome. If they could swim, they could have jumped up and swam in."
Mr Sertorio said the arrival of the boat had livened up the town. "You don't ever get to see any boat people in Geraldton," he said. "How they got this far down has got me beat."
Steve Ranch, who manages the local Dome cafe, said locals were stunned to see a crowded wooden fishing boat, about 20m long, approaching the shore. “At first people weren't sure what was going on,” Mr Ranch said.
Authorities are deciding where to house the asylum seekers tonight, with some suggesting a wing of nearby Greenough prison might be utilised.
“They have picked a really nice part of the coast to come ashore, and you do have to wonder how they get this far down the coast without being detected,” Geraldton mayor Ian Carpenter said.
“It will be an issue to find accommodation for that many people.”
Opposition border protection spokesman Scott Morrison said the boat's arrival was a sign of the Gillard Government's failure to protect Australia's borders.
“For locals in Geraldton, Labor's border protection failures literally came to their harbour this afternoon, and that is emblematic of the state of chaos that we have seen from this government on our borders,” Mr Morrison said.
“It is not funny at all, and this demonstrates the Government's border failures have got to the point that people think they can just turn up anywhere on our coast.
“The smugglers and those seeking to come know that this Government is a soft touch and it is open to all comers.”
Under existing legislation, asylum seekers who reach the mainland can avoid being sent to processing centres on Nauru or Manus Island in Papua New Guinea.
Federal Labor is seeking to change this, with legislation currently before the Senate.