The US star has called off an event at the London Palladium on 20 September, when she was to have been interviewed on stage by Sir Bruce Forsyth.
Minnelli was also booked to give a similar talk at Sheffield City Hall on 22 September.
According to reports, the events were cancelled due to a dispute over money with their promoter, Rocco Buonvino.
The promoter has previously organised celebrity appearances in the UK by Sylvester Stallone, John Travolta and others.
"We have been advised by the promoters of An Evening with Liza Minnelli that the performance has been cancelled," the London Palladium said in a statement. "All tickets will be refunded."
Rocco Buonvino Productions and Minnelli's representatives have not responded to a request for a comment.
Minnelli, the daughter of Hollywood legend Judy Garland and director Vincente Minnelli, won an Academy Award for her role in 1972 film Cabaret.
She is one of a handful of stars to have won the so-called Egot - an Emmy, a Grammy, an Oscar and a Tony.
In March, the 69-year-old was admitted to a drug and alcohol rehabilitation unit for treatment of substance abuse.
In promotional material issued when the shows were announced, Minnelli said she considered the UK to be "a second home".

Marco Goncalves, 34, assaulted the referee after being sent off in last month's game against Rio Tinto, and was escorted off the pitch by police.
Images of the attack went viral, with the referee suffering a broken nose.
Goncalves plays for Canelas, a club made up of FC Porto ultras who have been branded "thugs" for their aggressive style of play.
Three members of their squad, including the captain, hail from the 'Super Dragons' ultras, a well-known fan group of Porto.
Other clubs in the fourth-tier amateur league would rather pay a 750-euro fine and forfeit the match than play Canelas.
As a result, they are top of the league after a string of default wins, but no official complaints have yet been filed against the club.
A spokesman for the Porto regional league told AFP Gonclaves has been banned for four years for the attack on the referee, three months for assaulting an opposition players and two months for "insults".

Tourism NI said it expects a strategy to be in place by early next year.
Janice Gault from the Hotels Federation told the BBC's Inside Business programme it was crucial for the industry.
She said a "partnership" approach was essential.
"I mean we've really urged people to get a strategy at sort of quite a high level so that everybody can buy into that," she said.
"Hotels have probably spent about a billion pounds in the last decade and are set to spend more."
Ms Gault said another big boom was expected in the hotel market which would probably generate another half a billion pounds.
"The funny thing about the strategy is we still have the target, but we don't have the strategy. We only have one way to go and that's growth and the way for us to get that is to partnership," she added.
Singer and actress Liza Minnelli has cancelled two upcoming appearances in London and Sheffield.
[NEXT_CONCEPT]
An amateur footballer in Portugal has been banned for more than four years after kneeing a referee in the face.
[NEXT_CONCEPT]
The Hotels Federation has called for a proper tourism strategy for Northern Ireland to help boost growth in the sector.