Nationwide Building Society customers with cash card accounts will now have to take out a minimum of £100 if they use the counter service in its branches.
The new limit only applies to those with the most basic card account.
It does not include customers with pass books or debit cards.
Customers with cash card accounts will still be able to take out smaller amounts, but only by using a cash machine.
The move brings Nationwide in line with a number of its competitors, who already have similar - or stricter - restrictions on counter service use in place.
For example, Santander has a minimum withdrawal of £300 across most of its outlets, which include the Abbey. Alliance and Leicester will introduce the limit at the beginning of July.
At HSBC, basic bank account holders cannot make cash withdrawals at the counter, but they can make other transactions.
The change affects a third of Nationwide customers with Flex or Cashbuilder accounts.
The building society said the change was needed to reduce queues in its branches and that there were alternatives for those affected.
Nationwide says about a third of all counter transactions are carried out by less than 8% of its customer base.
The Payments Council, which sets the strategy for UK payments, says banks are simply responding to changes in customer behaviour.
Its director of communications, Sandra Quinn, says that 85% of people in the UK use cash machines to take out their money and Nationwide is simply reflecting that fact.
But Michelle Mitchell, Age UK's charity director, said the changes would not suit the habits of older people.
"Banks imposing minimum over-the-counter withdrawals to drive people to ATMs could be causing problems to some older people who find the chip and Pin system difficult to use or who have security concerns about using a cash point in the street," she said.
She added that people on low incomes often preferred to withdraw small amounts of cash in order to budget more easily - and said £100 was far too high, since it was more than the basic state pension.
Nationwide spokeswoman, Tina Coates, said that the majority of its branches had cash machines inside them and there was plenty of personal assistance on hand for people who needed a reminder of their Pin number, for example.
She said that the move was not a move against elderly customers, and only 5% of those with the simple cash card account system were over 70.
"ATMs have been around for over 30 years, we understand Age UK's concerns but not every elderly person is uncomfortable using cash machines."