Staff at Stiperstones National Nature Reserve (NNR) issued their appeal on Facebook after hearing that fireworks had been set off on the main track last Thursday evening.
"This poses a huge fire risk, as well as scaring the sensitive wildlife that lives here," they posted.
"Consequently, a local farmer’s sheep is now dead."
Stiperstones NNR includes the major part of the Stiperstones ridge in south Shropshire, near the Welsh border.
There is open and well-used public access to the reserve, including the Stiperstones Stomp 8km path and a number of shorter alternatives plus a 650m all-ability trail.
But last week's incident is not isolated, they say.
"We appreciate that most of our visitors are responsible, and it is the few that need reminding that this is a NATURE RESERVE, and visits should be for quiet enjoyment of the wildlife only," the Facebook post continued
"Any information regarding this incident is welcomed, and we have already involved the police in this matter," they add.
Contact details for the nature reserve are at facebook.com/StiperstonesNNR/.