Its chief executive, Michael Luscombe, said prices could sink as low as $1.50 a kilogram, down from yesterday's NSW price of $3 and a national average of $2.50.

He said the influx of cheap fruit was triggered by the mass planting of new banana trees to replace those lost in Cyclone Larry in Far North Queensland in 2006.

The discount prices are expected to last for about a fortnight.

"It's not an exact science," Mr Luscombe said.

"But I think a couple of weeks is what the growers are saying.

"It depends how quickly [customers] can eat bananas … I would imagine it would be a few weeks."

Rival supermarket chain Coles was yesterday unable to say whether it would also be offering cheaper bananas.

After Cyclone Larry, banana prices across all retailers skyrocketed, peaking at $15 a kilogram before falling back to $2 a kilogram nine months later.

Mr Luscombe predicted prices would hover between $1.50 and $1.80 a kilo, depending on wholesale prices, supply and shopper demand.

He declined to reveal the profit margin on bananas, or how much Woolworths would pay wholesalers for the fruit, but agreed the wholesale price would be more than $1 a kilogram.

Bananas used to be Woolworths' biggest food category, in terms of percentage of sales by a single item, but have been overtaken by tomatoes.

In an average week, bananas make up "well over 10pc" of Woolworths fruit and vegetable sales, Mr Luscombe said.

The company buys most of its bananas from north Queensland, as well as some from Carnarvon in Western Australia.

The price cut comes as Japanese supermarkets have run out of supplies because of the popularity of a diet which advises a breakfast of bananas will trigger weight loss.