The US singer was admitted to hospital on Monday night "in excruciating pain", a day after being treated for dehydration and a stomach virus.
She apologised to her fans through social media.
"I flip, dance, fly, harness, silk, and scream my way through a total s**t show of awesomeness (no pun intended). Therefore, I need to be physically healthy and well in order to perform this show. I think all of you deserve the full show and me at my best."
Among the fans to watch her return was actor Hugh Jackman.
"The amazing @pink One of the best concerts I have ever seen! And, she's been sick all week. Inspiring." he said on Instagram.
Pink will return to Sydney after finishing the New Zealand leg of her tour, with promoter Live Nation announcing new dates for her cancelled shows.
The August 3 concert has been rescheduled for August 24, while the others have been moved to September 17-19.
