The hazardous material was discovered at a bonfire in Monrush after residents reported the find to the Mid Ulster Council.
The Council described it as a "serious health and safety issue".
A spokesperson from the Council said: "This was a reckless and indiscriminate case of illegal dumping which showed absolutely no regard for the safety of local people and is to be condemned.
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"The Council will continue to work closely with the local community and its partner agencies to address similar issues which arise in the coming months."
PSNI Superintendent Mike Baird said: "Following concerns raised by local residents, Police along with Mid Ulster District Council and the Northern Ireland Environment Agency identified a significant amount of asbestos waste that had been dumped near to the bonfire site at Monrush.
"Safety for everyone is paramount. While the physical removal of bonfire material is not a matter for police, we will assist other lead statutory partners if called upon to do so."
(CD/MH)
