The council said items commonly removed included letters, packaging, and other documents – items that would otherwise be used to bring criminal cases.
While it was understandable people are frustrated by fly-tipping, it said the dumped rubbish should be treated as a crime scene and left alone.
“The public’s most valuable role is to report incidents promptly, ideally with photographs,” it said.
David Vasmer, the Shropshire councillor responsible for highways and waste, said: “When evidence is removed or shared online, it can completely undermine our investigations and allow offenders to go unpunished.”