The High Street lender is now offering the non-binary "Mx" prefix on its forms.
It said the option will be available to customers opening products such as current accounts, as well as staff.
Metro said it has made the changes in response to feedback from staff and customers and that it could react quickly because it was relatively new.
Danny Harmer, its chief people officer, said "making sure our customers and colleagues feel comfortable and accepted is a real priority for us".
She added that she hoped Metro's move would encourage others to follow suit.
A spokesperson for LGBT lobby group Stonewall said: "The changes that Metro Bank has made to its forms give important and much-needed recognition to people who do not identify as either male or female. It's great to see them taking proactive steps to ensure their needs are met and that they are accepted and included."
Other companies including Royal Bank of Scotland also allow customers to be identified as Mx rather than Ms, Mrs and Mr.
Last year the Oxford Dictionaries website added the Mx honorific, defining it as "a title used before a person's surname or full name by those who wish to avoid specifying their gender or by those who prefer not to identify themselves as male or female".
In September music streaming service Spotify began allowing users in the UK, US and Australia to choose "non-binary" rather than male or female.
Facebook gives users the option to select a gender other than male or female, and pick a pronoun from "he", "she" and "they".
The Beyond the Binary magazine is conducting a survey on UK non-binary people's experiences of organisations both in the workplace and as consumers. It is open until 19 December.
Metro Bank is the latest organisation to let customers choose an honorific that is neither male nor female.