Producers of the Simon Cowell-approved show have said that despite receiving good reviews on its opening, they will shut the doors on the production in May.
A statement described the closure as "sad" but insisted that the cast, crew and whole production team are "immensely proud" of what they have achieved.
"The West End can be an unpredictable place as the closure of a number of high profile productions recently has shown," said Rebecca Quigley, the CEO of Stage Entertainment UK.
One such production was the Spice Girls-inspired musical Viva Forever, which closed after six months.
"I Can't Sing! has had audiences on their feet night after night, four and five star reviews from the critics and an amazing company and creative team, but it seems that isn't always enough," continued Rebecca.
"To open any big musical, and particularly a brand new British musical comedy at the London Palladium, is no mean feat and hundreds of dedicated people have played a part in bringing this unique and wonderful show to the stage. I thank every one of those people and the audiences who have come to see the production."
I Can't Sing was co-written by Harry Hill and opened with the approval of X Factor boss Simon Cowell, who was guest of honour on opening night.
It stars former EastEnders actor Nigel Harman as an over-exaggerated character loosely based on Simon, and follows the journey of a young girl who auditions for a talent show and has her life changed overnight.
Simon has yet to comment on the closure, but Nigel Hall from Simon's Syco Entertainment production company has thanked the cast and crew for the "fun" show.
"From the moment Harry Hill and Steve Brown told us their idea for I Can't Sing we knew this was going to be a fun project," he said.
"Alongside Stage Entertainment we'd like to thank the cast and crew who have worked so hard on this show. To everyone at Really Useful Theatres and the ever supportive staff at the London Palladium, and everyone involved in I Can't Sing! I'd like to say a huge thanks and the very best of luck with their next venture."
The final show will be on Saturday, 10 May. Ticket holders for dates after that should contact their point of purchase.
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