An anticipated rate hike in the United States, which would strengthen the greenback, would contribute to that weakness, he said.
"Sixty cents against the US is very possible."
The New Zealand dollar hasn't traded at US60c since May 2009.
ANZ said it expected at least one more OCR cut before the end of the year, with a 50 per cent chance of a second.
The bank expects the currency to fall below US70c towards its trade target of US68c.
McCarthy said he expected the New Zealand dollar to eventually begin regaining strength against its US counterpart.
"As the global economy normalises we're likely to see currencies move back towards the middle of their longer-term ranges - and for the kiwi that means somewhere between 70 and 80 rather than between 60 and 70."
The New Zealand dollar fell more than 2c against the Aussie dollar after today's rate cut and recently traded at A90.32.