More than 2,300 people have signed a petition demanding that the council reopens its recycling centres.
Facilities across the country have been closed because of COVID-19 and the council has warned that flytippers face a £200 fixed penalty.
But petition organiser Tom Daniels insisted skip centres could operate safely if managed properly.
He said: “One member of staff could control vehicle entry while another ensures the required social distancing as residents dispose of their waste.
“For us all to hoard general waste in our gardens or communal areas creates immediate health concerns for families, neighbours and communities.
“Fly tipping has increased with temporary dumps a ticking time bomb of disease and infection.
“We are all living with one crisis and don’t need another.
“As residents and taxpayers, we need North Lanarkshire Council to see common sense and re-open these centres.”
The council said it is only following national guidance on non-essential car journeys and social distancing.
A spokesman stated: “We can’t do anything that increases the risk of transmission.
“However, we are developing plans to re-open our household recycling centres quickly if the government guidance on essential journeys changes.”
