What’s Love Got To Do With It? – named after one of Turner’s best-known songs – was set to visit the City Hall on April 18.
But, as the venue is shut temporarily, the performance has now been rescheduled for December 16.
Ticketholders are being contacted directly by box office staff. According to the City Hall’s website, the date change means the postponement meets the venue's criteria for a refund.
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A spokesman for the show said: “As everyone is aware, due to Government advice theatres and venues across the UK have had to take the decision to close. This inevitably affects our shows and therefore What’s Love Got To Do With It? has had to be rescheduled.
“We apologise for any inconvenience this causes and we hope you can join us on the rescheduled date.”
The show celebrates Turner’s 60-year career, and is led by the team behind the similar production Whitney - Queen Of The Night.
Coincidentally, the last-ever gig by the real Turner, now aged 80, happened in Sheffield in 2009. Her final tour - a 50th anniversary trek that grossed $130 million - finished with a date at what is now the FlyDSA Arena, after which she went into retirement.
Speaking to Graham Norton in 2018, she said: "We had the greatest show, it was really wonderful. But the next day... I took a deep breath and said 'This is it, I'm not going back for anything'."