The problems affected Nationwide customers logging in to see their current and savings account balances from around 8am, and lasted for about an hour.
Nationwide, whose advertising slogan is "On your side", said the hitch has been fixed and it has apologised to customers for any inconvenience.
Consumers vented their annoyance and some pointed out that many people need to check their wages are being paid in at around this time of the month.
One Twitter user said: "Tried to log into online banking this morning to get told 'it doesn't look like you have an account with us'."
Another wrote: "Seems I'm not the only one who happens to have lost their #Nationwide accounts this morning online."
Nationwide posted an apology to customers on Twitter, saying: " Some customers were unable to access accounts this AM due to a technical fault. This has been fixed & we apologise for any inconvenience."
A spokesman for the building society could not give a figure for how many customers were affected but said it was a relatively small number.
Nationwide has said the recent jump it has seen in people looking to switch to it follows a strong period of growth in its market share of current accounts in recent years, which coincided with several major scandals involving big banks.
The building society suffered a similar technical problem in April, when customers were locked out of their online accounts. Last year, nearly three-quarters of a million Nationwide customers saw debit card payments taken from their accounts twice. These mistakes were later corrected.
Lloyds Banking Group also had technical problems earlier this month, which to its embarrassment were on the first day its new TSB branches launched on to the high street.