ANZ boss Shayne Elliott says he will personally apologise to a former US employee over her treatment by lawyers acting for the bank.
The unnamed former senior trader was questioned about being raped as a teenager, Fairfax Media reports.
The questioning was part of the bank's defence in a discrimination claim against ANZ and its head of corporate sales in America, Ravi Nursey.
Mr Elliott tweeted "a serious line was crossed" after the news broke on Saturday.
He added the bank had instructed the external lawyers not to use the information, from a deposition last year, as part of the bank's defence in a looming trial relating to the woman's allegations of sexual and racial harassment at ANZ's New York office.
"I apologise. This is wrong & not acceptable. We were not aware of our external NY lawyers strategy & should have been," Mr Elliott wrote on Twitter.
"I will apologise to the complainant personally."
Fairfax reports the former trader was questioned about being sexually assaulted while attending university in the US, her sexual history and if she had ever had a sexually transmitted disease.
A lawyer acting for ANZ defended the questions and implied the woman may have overreacted to an incident, Fairfax also reported.
In a statement, ANZ said "we are aware that the law and practice in the United States is different to Australia".
"However, the questioning was not consistent with our culture or values and we don't consider (the former employee's) past sexual history or her being the victim of sexual abuse relevant to our defence".
The bank added the external lawyer concerned had switched firms and was no longer involved in the case.
Australian Associated Press