The company has blamed the move on the high cost of distribution of the items and difficult trading conditions, with a sharp fall in the market value of recyclables.
A notice was delivered into homes across the city giving the bad news.
In the leaflet, householders were told they could buy special Greyhound-branded recycling bags from a list of almost 40 approved retailers in Dublin 1, 2, 3, 4 and 6.
"The price is the cheapest in the market," a Greyhound spokesman insisted.
He added: "The business was losing €12m per annum when Greyhound took it over from DCC. We have identified this as one loss-making part of the business."
It is the latest controversy to hit the bin collection service since its privatisation.
Families who do not have space for green bins have no choice but to use the Greyhound bags as the company says it will not collect recyclable waste in future unless it is presented in the branded sacks.
The move comes days after the City Bin Company said it will expand into the area managed by Dublin City Council as it takes on rival Greyhound.
The company said the first 5,000 customers to switch will pay just €99 for waste collection next year, as it seeks to build up market share.
"The people of Dublin city are deserving of a much higher-quality of service from their waste collector than what they have been used to," City Bin head Gene Browne said.