The singer was due to start The Truth Is tour in September, which would run for 13 days.
In a statement posted to her Twitter page she said that she had made the decision after spending “a few days away”.
“The timing just wasn’t right. I’m really sorry to anyone who has been inconvenienced by this decision”.
She also added, “I love performing more than anything and can’t wait to reschedule more live shows in the future.
“There will be more news coming from me soon.”
The former Strictly Come Dancing contestant has just finished playing Svetlana Sergievsky in the West End production of Chess and was due to perform songs from her album, which was released in March.
A statement on her website said that full refunds would be issued to everyone who had purchased tickets.
The BBC has contacted a representative for Burke for comment.