"To me, a bank should provide services to the public and help the needy, but not to bully those whose accounts do not hold a minimum balance of $100,000 at any one time."
The customer said he had approached the Human Rights Commission over the matter.
The letter he received from HSBC New Zealand's head of retail banking, Glen Tonks, said he may like to consider upgrading to Premier if he would like to stay with the bank.
"At HSBC we periodically conduct reviews of our products and services to ensure we continue meeting the needs and requirements of customers appropriately," Tonks said.
"We are therefore writing to advise you that we are withdrawing non-premier banking services. Unfortunately this means your non-premier account(s) will need to be closed."
An HSBC spokesman said the bank couldn't disclose how many customers were affected by the change as that information was commercially sensitive, but it was a "small number".
He said the HSBC Premier criteria were well publicised in the bank's marketing materials.
HSBC's operations in New Zealand were focused on wealthy clients and the bank's business model was not suited to those who didn't meet the Premier criteria, the spokesman said.
He said their needs could be better fulfilled by other banks which "provide banking services for regular retail customers".
HSBC, like many of its global counterparts, is facing a tough operating environment as a result of a range of factors such as stubbornly low interest rates and geopolitical and economic uncertainties including Brexit.
Group chief executive Stuart Gulliver has cut HSBC's workforce from 296,000 to about 250,000 since he took over in 2011.
In August HSBC announced a two-year fixed home loan rate of 3.79 per cent, thought to be this country's lowest rate in at least 50 years.
The rate was only available to Premier customers.
