Such energy users are typically more vulnerable to fuel debt, and currently face a charge of up to £900.
As many as 4.5 million people use prepayment meters for electricity, while 3.5 million use them for gas.
Prepayment meters provide pay-as-you-go access to electricity and gas, and can be installed by an energy supplier when a customer falls into debt.
By paying for fuel in advance, it means the customer cannot run up further arrears.
Consumers who pay in advance also face higher energy bills, although from April 2017 these prices will be capped.
Suppliers can be permitted to charge for the installation of a meter.
Such charges are typically £400, but can be as high as £900 when court costs are included.
While some suppliers do not charge anything at present, Ofgem is suggesting that the maximum fee should be between £100 and £150.
For particularly vulnerable consumers, such as those in financial hardship or those with health issues, it says there should be no charge at all.
Scarf has welcomed the proposal.
Garry Donald, Team Leader of our Home Energy Advice Team, said:
“We support people living with fuel debt and installation fees exacerbate what are already challenging financial circumstances.
“To cap the fees or remove them would ease the strain on the household budget, giving people a better chance of tackling their debt.”