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Australian network Ten released a statement saying Breakfast, which is fronted by Henry and Australian journalist Kathryn Robinson, will cease production on November 30.
It admitted the show had failed to catch on with viewers.
"Breakfast television still represents an opportunity for Ten and we will return to the breakfast TV market at some point next year," the statement said.
Henry and his former New Zealand Breakfast co-presenter Pippa Wetzell have been tipped to replace presenter Mark Sainsbury once Close Up is axed later this year.
Breakfast has been a very distant third in the early morning slot this year.
The Seven Network's Sunrise has averaged about 365,000 viewers each day in 2012 and the Nine Network's Today has averaged around 330,000.
Meanwhile, Breakfast, which debuted in February, has an average daily audience of about 40,000.
In October a Ten spokesman said Breakfast would screen in 2013 despite poor ratings.
But on Monday morning the news and breakfast teams were told that the shows would cease at the end of the month.
Replacement shows for 2013 have not been announced.