One cyclist was injured slightly when riding his bike in Ransom Wood off the Rainworth bypass in Nottinghamshire.
Officers are also concerned that if a motorcyclist hit the wire they could be seriously, if not fatally, injured.
Pc John Albanese said: "If they hit the wire at anything faster than 10mph they would be seriously injured, perhaps even decapitated."
He added: "It could be the work of a prankster, but it is more likely a crude attempt to stop illegal off-road bikers from using the path.
"It may seem a justified course of action to whoever did this, but their method is very dangerous and could cost someone their life."
The 37-year-old cyclist was saved from severe injury by his helmet, which took the force of the impact with the head-height wire.
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