Big Six provider SSE said it had launched an urgent investigation into the errant devices, one of which warned a customer they had bust their daily budget by nearly three million per cent.
Complaints began appearing on the company's Twitter page on Friday, with dozens of customers eventually saying their meters were quoting thousands of pounds for 24 hours of gas and electricity.
One account holder tweeted SSE with a photo that said they had used Â£33,183 of gas in one day - 2,765,175% over budget. The following day the meter said the bill would be Â£27,022 for the day.
The average annual bill for a medium-sized house in the UK is around Â£830.
The customer said: "Prices certainly gone up @YourSSE @SSE if my smart meter is accurate on my gas use over last few days! like it warm but .."
Another customer, Usman Hussain, tweeted a picture of his meter saying he would be charged nearly Â£9,600 for his day's electricity and gas.
SSE said it was aware of an issue affecting "a small number" of its smart meters.
A spokesman said: "The issue will be investigated as a matter of urgency and no customer will be charged the extra amounts resulting from errors with the smart meters.
"We would like to apologise to any customers if this has caused distress."
Smart meters communicate directly with energy suppliers, allow customers to monitor their energy use in real-time and eliminate the need for estimated billing.
The Government hopes the devices will be rolled out to every home in Britain by 2020.
The latest figures show there are 4.9 million meters in homes and businesses across the country.