Vic Toews, Canada's public safety minister, said on Thursday that there were 490 people aboard the ship, possibly including members of the LTTE.
Some of those on the ship are "suspected human smugglers and terrorists", Toews told the broadcaster CBC, adding that Canada would prosecute anyone involved in human trafficking.
Canada and other Western nations have been critical of Sri Lanka's human rights record, but consider the LTTE - defeated last year after a two-decades long war- to be a terrorist organisation.
Al Jazeera's Nick Spicer, in Washington, DC, said the migrants were being processed by police and that those sick would be sent to hospital.
"There have been rumours that some of the passengers on the boat may have infectious diseases," he said.
"There was a rumour of tuberculosis. All that will be checked out.
"The expectation is that [they will] then be sent to jail and then they will be able to claim refugee status and be allowed to live in Canada."
After days of tracking by Canadian and US authorities, the Canadian navy and immigration officers on Thursday boarded the ship as it neared Vancouver Island.
Calls for compassion
Sri Lanka's high commissioner to Canada has asked the country to reject their refugee status, calling it a human smuggling operation linked to the rebels.
Canadian Tamils have urged authorities to accept the asylum seekers, saying that the minority group faces continued difficulties in Sri Lanka.
Krisna Saravanamuttu, the spokesman for the National Council of Canadian Tamils, said "these people are fleeing from persecution and they must be treated with compassion".
"They must have went through hell and high water to ensure they could escape Sri Lanka," he told CBC.
"There are severe health problems on this ship, and many of the individuals on this ship are under the age of 13."
There are unconfirmed reports that one person died on the ship.
Many members of Sri Lanka's Tamil community allege discrimination in their homeland.
Sri Lanka has repeatedly rejected a United Nations probeinto alleged rights abuses during the final stages of its long civil war, which ended with government troops defeating the Tamil Tigers in May 2009.
According to the UN, at least 7,000 ethnic Tamil civilians were killed in the last four months of the civil war, while rights groups have accused the government of deliberately shelling civilians.