Chief Censor David Shanks required the warning note be updated to include 'suicide' after receiving complaints including from the Mental Health Foundation.
The Police Victim Support team first advised that two vulnerable young people had been 'severely triggered' by the movie.
The Mental Health Foundation had also told them about a number of complaints they had received.
The method of suicide used in A Star Is Born was the most common method of suicide in New Zealand, Shanks said.
Shanks said A Star is Born handled the topic relatively sensitively, the OFLC felt it was in the best interest of the NZ public to add the warning particularly considering New Zealand's appalling suicide rate.
"Many people in New Zealand have been impacted by suicide. For those who have lost someone close to them, a warning gives them a chance to make an informed choice about watching."
Mental Health Foundation chief executive Shaun Robinson said they had received dozens of complaints about the movie and most were around the fact that viewers weren't warned there were significant suicide scenes in the movie.
"By not being adequately warned they couldn't make a choice to expose themselves to that or not. I think that was the major issue."
He said for those who were going through challenges that were leading them to think about suicide and to be exposed to images or messages about suicide can be really disturbing for them.
"Some people have been really quite affected by it and not just feeling bad, but actually activated anxiety and had to seek professional help. So this is actually quite a serious issue. It's not just a passing thing or a mild reaction."
The film was one of several films and TV shows including 13 Reasons Why that had upset Kiwi viewers, he said.
Robinson said New Zealand's censorship laws were out of date and he wanted OFLC to have the ability to be more proactive and censor not only films, but also other online series.
He was pleased a warning had been added, but said it was a pity the censor had not been ability to give the warning before it was publicly viewed.
"I think to a certain extent the horse has bolted now for many people, but better late than never I guess."
A Star is Born is a re-make of a popular film first screened in 1937.
The film tells the story of seasoned musician Jackson Maine (Cooper) discovers, who falls in love with struggling artist Ally (Lady Gaga), coaxing her into the spotlight.
As Ally's career takes off their relationship breaks down, as Jackson confronts his internal demons.
WHERE TO GET HELP:
If you are worried about your or someone else's mental health, the best place to get help is your GP or local mental health provider. However, if you or someone else is in danger or endangering others, call police immediately on 111.
OR IF YOU NEED TO TALK TO SOMEONE ELSE:
• LIFELINE: 0800 543 354 or 09 5222 999 within Auckland (available 24/7)
• SUICIDE CRISIS HELPLINE: 0508 828 865 (0508 TAUTOKO) (available 24/7)
• YOUTHLINE: 0800 376 633 ,free text 234 or email talk@youthline.co.nz or online chat.
• NEED TO TALK? Free call or text 1737 (available 24/7)
• KIDSLINE: 0800 543 754 (available 24/7)
• WHATSUP: 0800 942 8787 (1pm to 11pm)
• DEPRESSION HELPLINE: 0800 111 757
• SAMARITANS – 0800 726 666.
