Its chief executive, Jonathan Brearley, said the price cap, which limits how much energy providers can charge per unit, would go up again because of the “unprecedented” rise in gas prices.
The cap is revised twice a year and is next due to be changed in April.
Natural gas prices are at record highs as economies around the world begin to recover from the Covid crisis.
As a result, firms that supply gas to householders are running into trouble because they have agreed to sell energy at less than the price it now costs them to buy it.
Last month, nine of those companies went out of business, forcing 1.7 million customers to move to new suppliers.
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Ofgem’s Mr Brearley told the BBC that the price cap was there to stop firms making unfair profits, but “legitimate costs have to be passed through”.
He said it was too early to say how much the rise in April would be or whether Ofgem would have to review the price cap more frequently in future.
However, he added that the regulator might have to look at the formula according to which the cap was set.
His warning comes as domestic customers are still reeling from the latest price cap increase, which took effect for households in England, Scotland and Wales this month.
Households in Northern Ireland have also seen a recent sharp rise in their bills, but they are not protected by the energy price cap for Great Britain.
That was the biggest jump, to the highest amount, seen since the backstop was introduced in January 2019.
Those on standard tariffs, with typical household levels of energy use, saw an increase of £139 – from £1,138 to £1,277 a year.
Prepayment meter customers with average energy use saw a £153 increase.
The next revision to the energy price cap will be decided by Ofgem in February, but will come into force in April.
Analysts Cornwall Insight said that the cap could go up by £400, meaning that a household with typical energy use would pay about £1,660 a year.
On Thursday, National Energy Action, a charity, said that between 1.2 million to 1.5 million additional households could be hit by fuel poverty next year.
While the price cap helps households, there is no such safeguard for businesses, which have to absorb the full impact of rising global energy prices.
They have called for government help to control costs and keep plants open.
Mr Kwarteng said on Twitter protecting consumers from rising global gas prices was “his top priority”.
He also announced he would meet the Energy Intensive Users Group (EIUG) on Friday.
The group includes representative bodies UK Steel, the Chemical Industries Association, the Confederation of Paper Industries, the Mineral Products Association, the British Glass Manufacturers Federation, the British Ceramic Confederation, BOC, Air Products and the Major Energy Users Council.
Last month, high gas prices forced two fertiliser factories to close, cutting supplies of carbon dioxide which is widely used in food production.