In a statement, Westpac spokesman Chris Mirams said "processing of payments has been completed to other banks".
"All impacted automated payments will be honoured and no customers affected will be left out of pocket."
Westpac did not initially respond to phone calls about the incident but appeared to be tweeting to some customers as social media sites lit up following the fault.
The bank will not say how many customers were affected.
People had used Twitter to detail a technical fault from the bank which meant overnight payments to a number of other banks had not been processed.
"Tech issue with o/night payment processing means some payments have not been processed as planned. We're investigating & will resolve ASAP," Westpac tweeted.
The bank also tweeted it would waive or reimburse any costs incurred by their customers as a result of the fault.
"We apologise to any customers impacted by payment processing issues. Any fees, charges or interest occurring as a result will be reverse." (sic)
ASB also tweeted: "Some overnight payments from Westpac haven't been processed to ASB & other NZ banks. Westpac is urgently investigating, we'll keep you posted."
BNZ's customers also got a Twitter assurance that any fees incurred as a result of the glitch will be refunded.
Twitter posts suggested Kiwibank and National Bank customers had also been affected.
It is the second time in the past year the bank has had this kind of problem, raising questions over whether it should remain the Government's banker.
"If there's been some sort of service failure we wouldn't be waiting around for a review of the contract," Acting Prime Minister Bill English said.
"People should be getting paid correctly on their pay day."
Some MPs, including Labour's Chris Hipkins, got caught up in the glitch.
"I did notice it late last night," he said. "Thankfully my mortgage repayments don't go out until the day after the pay goes in so it didn't create a huge headache for me."