"ANZ Bank New Zealand will increase the interest rates on its floating and flexi home loans by 0.15 per cent," it said in a statement.
This would add about $10 a week to a $350,000 home loan.
ANZ would also increase interest rates on a number of savings and call accounts including online accounts from October 12 and its serious saver accounts from November 1.
The RBNZ monetary policy committee said the current Covid-19-related restrictions had not materially changed the medium-term outlook for inflation and employment since the August Statement.
Capacity pressures remained evident in the economy, particularly in the labour market.
"While the economy contracted sharply during the recent nationwide health-related lockdown, household and business balance sheet strength, ongoing fiscal policy support, and a strong terms of trade provide confidence that economic activity will recover quickly as alert level restrictions ease. Recent economic indicators support this picture," it said.
The New Zealand dollar rallied by about 25 pips to US69.75c on the news, while bond yields remained largely flat.
"It seems from the currency's reaction that people are running with the action, which is that they have begun," Hamish Pepper, fixed income and currency strategist at Harbour Asset Management said.
"They have hiked, and suppose there is something in that."
KiwiBank chief economist Jarrod Kerr described the move as the start of a "new chapter" for the cash rate as it moved off its historic low of 0.25 per cent.
"The RBNZ won't stop here," he said.
"We expect 25 basis point hikes will be delivered in October, November, February and May, with the OCR reaching 1.50 per cent by the middle of next year. We expect a considered pause around 1.5 per cent. Although the RBNZ is signalling a continuation to 2 per cent in 2023."
ANZ senior strategist Daivd Croy said the market had priced in a 90 per cent chance of a quarter-point hike and there was a slight upward movement in the short end of the yield curve when the rate change was confirmed.
"I think the Reserve Bank played it with a pretty straight bat. It's hard to argue with any of their assessments.
"There is a degree of caution in there, particularly around how the Delta situation plays out locally.
"They also acknowledge that there are capacity pressures and inflation pressures there as well."
Croy expects the bank to hike again at its next opportunity in November, but he said expectations of rate hikes in 2022 would be pared back somewhat.
"I think we can assume that we are going to get a followup rate hike in November, but if the health situation deteriorates, hikes in 2022 become less certain," Croy said.
- Additional reporting Jamie Gray
