The 30-year-old star - who has daughters Ethel Mary, three, and Marnie Rose, two, with husband Sam Cooper, who she wed in 2011 - was wrapped in a foil blanket and given oxygen following the incident, which "lasted about 45 minutes", before she was driven away by Cooper.
Another onlooker told The Sun newspaper: "She was in the recovery position and two security guys were talking to her. It looked like they were trying to get people away from her. She looked in a bad way, she was pretty f***ed.
"Before that I saw her staggering around looking haggard and out of it."
The musician - who released her third studio record Sheezus last year - has previously spoken about her tendency to take drugs at the festival, admitting she first dabbled with illegal substances while she was at the iconic event aged 13.
She previously said: "Glasto '98 was the first time I ever took drugs, so it was pretty incredible. Not that drugs are good, but if you do them in moderation then they're fine."
- Bang! Showbiz