Now visitors are being asked to take extra care to prevent further incidents.
A council spokesman said parks in Motherwell, Wishaw and Cumbernauld have been affected, with damage caused to plants, paths and wildlife.
Councillor Michael McPake, convener of the environmental services committee, said: “Our parks are blooming in this fantastic summer weather and visitor numbers are increasing, but this has also led to fires caused by vandalism or litter being dropped.
“The hot sun can easily cause dropped cigarettes or matches to ignite and fire spreads very quickly in the dry grass and woodland. Even a piece of glass can cause a fire.
“The effect can be devastating on the landscape within parks as well as to the wildlife, with young birds and animals trapped by fire or hurt by smoke inhalation. It can also create danger for people visiting parks or walking in the countryside.
“So we are appealing to residents to be particularly careful through the summer not to drop litter and to report any antisocial or suspicious behaviour to Police Scotland.
“Please help us to protect our wonderful parks and green spaces for everyone to enjoy.”