The herd is believed to have broken out of the northeastern Makgadikgadi Pans Game Reserve and strayed into a nearby village of Dukwi.
Village chief Kelethusitse Mosweu said one of the elephants brought down the electricity pole, which resulted in the transmission cables falling on the entire herd.
“Officials from the wildlife (department) came to my office late on Monday to notify me about the incident,” said Mosweu, who did not specify when the incident occurred.
The ministry of Wildlife, Environment and Tourism confirmed the accident and said it has launched an investigation.
Botswana has the largest elephant population in Africa at over 135,000, according to a 2015 count.
The International Union for Conservation of Nature (IUCN) has said the number of African elephants has fallen by around 111,000 to 415,000 in the past decade, the worst drop in 25 years.
And the killing continues at a dizzying pace of about 30,000 elephants a year.
