The independent body is responsible for monitoring implementation of the 10-year, $41-billion health accord struck in 2004.
But the council said it has been told there will no longer be a need for its work once that accord expires next year.
Chief executive John Abbott said Health Canada told him last week that funding would continue through this fiscal year, but come to an end after that.
"There's two tenets they've wrapped it in," Abbott said Tuesday.
"One is the federal fiscal environment. And because the current accord finishes next month, they felt our primary mandate would be complete and it was legitimate then to fold up the organization."
The council relies entirely on federal money to fund its operations, which include monitoring and reporting on the progress of the 2004 health deal as well as the 2003 First Ministers' Accord on Health Care Renewal.
Ottawa will continue to give the council $6.5 million for the remainder of this fiscal year, and $4 million to close up shop in 2014-15.
The decision to cut off funding caught the council by surprise, Abbott said.
"This did come right out of the blue."
Steve Outhouse, a spokesman for Health Minister Leona Aglukkaq, said the time is right to end the council's funding.
"The Health Council was largely operating around the health accord that was put in place around 10 years ago," Outhouse said.
"With that coming to a close, it's a natural time to wind down at least the federal funding for it."
Outhouse said the federal government is instead focusing its health spending "on patient-oriented research, things that are connected to front-line health-care service to Canadians, including transfers that go to provinces and territories.
"So it seemed like a natural time to make that transition."
When the current accord expires next year, the federal government will continue to increase its health transfers to the provinces for the next decade, but at a lower rate of increase, and with no strings attached.
Aglukkaq left the door slightly ajar to the council continuing its operations — just without any money from Ottawa.
In a letter sent earlier this month to provincial health ministers, who also act as corporate members of the council, Aglukkaq said it is up to the provinces and territories to decide whether to keep funding the organization.
"I should emphasize that this is a decision about federal funding for the council, and that formal decisions about its future as an entity will need to be made collectively by us, the council's corporate members," Aglukkaq wrote.
"I have asked my deputy minister, Glenda Yeates, to follow up with her provincial and territorial colleagues to identify a timely process for us to make these decisions."
Abbott said he sees a role for the council after the current accord expires. For instance, he noted, there will still be a need to hold governments accountable for health-care delivery and spending.
"Most of our reports were written so that the Canadian public could certainly have a better understanding of the issues at play and that they can use those reports to help hold governments accountable at the provincial and national level."
The left-leaning Council of Canadians called the funding decision "scandalous."
"The Council of Canadians views this as an intentional and very serious attack on the public health-care system in Canada and a clear indication that the federal government is not interested in the health of Canadians," Adrienne Silnicki, the group's health-care spokeswoman, said in a statement.
Canadian Doctors for Medicare also criticized the move.
"The federal government is no longer walking away from health care, it's sprinting at full speed," Dr. Ryan Meili, the group's vice-chairman, said in a statement.
"Cutting funding to the Health Council means cutting information on sustainability, quality and efficiency of our health care system — information that Canadians should be able to expect from their government."
NDP health critic Libby Davies said there remains a role for the council, so cutting its funding is a mistake.
"It's a lack of planning and a lack of foresight at minimum, and at worst, it's another indication that the federal government is abandoning its role in health care," she said.
"So I think either way you look at it, it's bad news."
Last year, Finance Minister Jim Flaherty abruptly unveiled a take-it-or-leave-it plan to pay for health care from 2014 to 2024.
The plan sees the federal government committing to a six per cent annual increase in funding for each of the first three years. After that, annual increases will be a minimum of three per cent — or more, if the economy is strong.