Mr Gela says the council has been forced to act because there are no health checks in place and he fears more people could die.
"My people are vulnerable and susceptible to contracting TB," he told AAP.
"Some of our communities are right on the front line, they're only a 10 minute boat ride from the PNG border.
"The reason is strong and simple: we're very, very concerned."
Health Minister Lawrence Springborg says Queensland isn't receiving enough compensation to treat the hundreds of sick people from PNG who travel across the border each year.
He begrudgingly signed a deal on Wednesday that will see the state receive $18 million in compensation from the Commonwealth over four years.
He wanted an extra $10 million a year and a commitment to close the north's "porous" borders.
"This border is about as porous as a spaghetti colander," Mr Springborg said.
In 2011/12 about 1100 Papua New Guineans visited Queensland Health facilities in the Torres Strait and Cairns, 15 of whom had tuberculosis.
In one case, the cost of a patient's treatment came to $1 million.
Mr Springborg says Mr Gela wants to close the border, but only the Commonwealth has the power to do that.
Mr Gela described the extent of the TB outbreak in the Torres Strait as an epidemic and says the situation has worsened over the past decade.
He welcomed funding for programs such as AusAid in PNG but says Australia needs to ensure the money is being spent on stopping sick people crossing the border.
"The Australian government is pouring money into an international country with very little measures ensuring accountability," he said.
Mr Gela warned authorities not to view Torres Strait as "out of sight, out of mind," as diseases that spread through that area would soon reach the mainland.
"This is everybody's business," he said.
"The state and federal governments need to front up to this issue and deal with it."
The Torres Strait and Northern Peninsula Hospital and Health Service says asylum seekers have been treated in far north Queensland hospitals.
Spokeswoman Simone Kolaric says a Syrian man, who came via PNG, was brought to a hospital by immigration officials a couple of months ago, amid concerns he had TB.
- AAP
