The Oscar-winning actress was speaking at the event in France when the interviewer asked her about the pattern of interlocking 'V's' on her left hand.
"Some people mind find it hard to believe, but you also have a tattoo - what's the story behind it?" the journalist asked.
"I got very drunk on a reservation," Mirren replied, laughing. "Does anyone ever get a tattoo when they're not drunk?
"It was done with a safety pin, it was so painful. Oh my god. Like a prison tattoo. It represents a very beautiful idea which is basically 'equal and opposite', that someone can be as different from you as you could possibly imagine, but have equal value to yourself, that's something I believe in life."
Mirren was among the women in film who took part in a red carpet demonstration on Saturday 12 May.
Cannes has consistently come under criticism for failing to showcase more films by women directors, but the pressure has been turned up amid the Time's Up and `#MeToo campaigns.
This is the first Cannes festival since allegations of sexual abuse were first made against producer Harvey Weinstein last year. He has denied all allegations of non-consensual sex.
An anti-harassment hotline has been created for the 2018 festival, with French Equality Minister Marlene Schiappa saying it had received “several calls” since the gathering began on 9 May.
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