The 64-year-old presenter and comedian, known for hosting the Great British Bake Off and QI, was due to begin the New Zealand leg of her tour on Sunday, visiting Christchurch, Wellington and Auckland.
A statement on Toksvig’s Twitter account said she hopes to return to the UK as soon as she becomes well enough to travel.
It said: “Due to illness, Sandi has cancelled the New Zealand leg of her tour.
“She has been admitted to hospital with bronchial pneumonia while still in Australia and is unable to travel & perform.
“Our main priority is getting her home to the UK as soon as she is well enough.”
Bronchial pneumonia is a type of pneumonia featuring acute inflammation of the bronchi, the two large tubes that carry air from the windpipe to the lungs, and is often accompanied by inflamed patches in the nearby lobules.
Her show, titled Sandi Toksvig Live!, is described as being “an evening of comedy and curiosities” in which she shares “little known facts” and tells “tall tales” alongside some “really silly jokes”.
Toksvig announced her departure as co-host of Bake Off in January 2020, saying she wanted to focus on other projects.