ScottishPower is appealing to criminals to stop the dangerous practice, saying it is only a matter of time before a life is lost.
About 20 incidents of thieves targeting power lines in farms and rural locations have been recorded across central Scotland in just over two weeks.
The company is warning that cutting down live power lines carrying up to 11,000 volts of electricity could cause fires or accidents.
Recently, 1,500 homes were cut off after a power line was brought down across a road and was struck by a truck.
A theft from a substation in Greenock, Inverclyde, last year caused two serious house fires with 200 homes cut off while engineers carried out safety checks.
In 2011 a botched cable theft in Glasgow resulted in a 30-minute power outage for 50,000 properties.
There have been more than 850 thefts since January 2011, with in excess of 70,000 homes exposed to the increased risk of faults or damage.
Guy Jefferson, network operations director at SP Energy Networks, said the recent thefts were "deeply concerning" and urged anyone with information to contact police.
He said: "Metal theft is one of the biggest threats to the safety of the electricity network and the impact of these crimes can be devastating.
"In recent years we have witnessed house fires and damaged electrical appliances in homes.
"One man died recently attempting to steal copper from an electricity pole in Lanarkshire and others have suffered horrific burns, loss of limbs and scarring.
"Unfortunately it seems like the thieves don't care about the risk to their own lives and they certainly show no regard for the safety of neighbouring properties."
Stolen metal is often sold on through scrap merchants before being exported around the world.
Mr Jefferson said the company hoped proposed legislation to prevent scrap metal dealers paying cash for materials would help stop the thefts.
Anyone with information on the recent spate of thefts is asked to contact police or ScottishPower's 24-hour hotline on 0800 092 9290.
The company is offering £20,000 for individual rewards for information that leads to a successful conviction for theft.