CNN affiliate Nine News reported Page collapsed toward the end of the concert.
"At the end of the show this evening there was a medical incident off stage involving Greg Page. Medics were called immediately and he was taken to hospital where he is receiving treatment," The Wiggles wrote on Twitter.
The Wiggles tweeted late Friday they had visited Page in the hospital.
"He's so grateful for the messages of love & support from around the world," the tweet read. "Greg's main concern was that the show tonight should go on. Let's do it for Greg whilst raising much needed funds."
The band were performing in a sold-out reunion concert in aid of three groups tackling the fires raging through Australia.
Dressing as Blue, Red, Yellow and Purple Wiggles, the band became hugely popular in Australia after they formed in 1991.
A new line-up was formed in 2013 to keep the brand alive, but the original Wiggles had not performed together for several years before Friday's concert.