She can be heard asking the band to stop and saying: "I'm sorry, there's fireworks in this one and I don't want to scare them".
Approximately 95,000 fans had made their way to the ANZ stadium and had to clear a path to allow paramedics to get to the ailing woman, who was taken to a local hospital in a serious condition.
She added that no one had noticed the woman had collapsed until Adele pointed it out.
"I wish you a speedy recovery".
During the show at ANZ Stadium here in Australia, the 28-year-old singer asked if anyone would be attending Bieber's concert being held at the same spot next week when crowd started booing, reported Cosmopolitan magazine.
She also joked that she had ruined the surprise for the rest of the audience by telling them about the pyrotechnics.
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She said: "At this point in the show last night, there was a lady, she got really ill down there and I sang this song and with my back to what was going on". Adele told the crowd.
The source said, "She actually seemed really tearful".
"Obviously I can't go through with those feelings because I'm married now".
Adele and Bieber's music tours happen to coincide in Australia.
The Grammy victor was performing to one of her biggest crowds to date, with 95,000 people in attendance, when the incident occurred.