Multi-policy discounts applied when someone had more than one risk or cover insured under one policy, or under multiple policies.
Between April 2014 and May this year, Vero and its intermediaries issued invoices to about 47,000 customers and overcharged $8.7m in premiums, the authority said.
The financial regulator claimed Vero failed to apply discounts due to errors and deficiencies in its systems.
The FMA said those deficiencies included data entry errors by Vero employees and some intermediaries selling the policies on behalf of Vero.
It alleged that liability primarily rested with Vero as it designed, owned and maintained the systems at fault.
Vero reported the issue to the authority in December 2019, when its remediation programme had been underway for several months.
But the FMA said Vero had not fully reviewed all affected intermediary channels, so the authority requested the insurer carry out a full investigation and remediation plan.
Vero subsequently discovered even more affected customers.
The authority said Vero had already reimbursed $10,259,000 in overcharges to affected policyholders.
"The scale of customer harm caused by Vero's system failures is significant," FMA enforcement head Margot Gatland said today.
"And we consider Vero was slow to investigate the issue, despite even being pressured at one point by one of its intermediaries," she added.
"Vero was aware from 2010 that there were issues with its systems but failed to adequately recognise their magnitude."
Vero today said it identified the issue as part of its regular internal review processes and self-reported it to the FMA in 2019.
Jimmy Higgins, Vero chief executive, said any negative impact on customers was unacceptable.
"We are sorry for the impact this has had on some customers. Our priority has been to make it right for customers, and we have been working hard to contact anyone impacted, whether they still have a policy with us or not," Higgins said.
"We remain focused on fixing any issues we find as quickly as possible and continue to look for ways we can deliver great outcomes for customers."
Vero said the problematic issue was no longer occurring and the company was working proactively with intermediaries to fully reimburse both past and present customers for any due discounts.
"To date, the vast majority of customers impacted by this error have been remediated and apologised to," the insurer said.