In a statement on Twitter, the band said it was "with great regret, due to illness, we cannot perform at Customs House Belfast".
Organisers said they were working to re-schedule the concert.
Many concert goers said they were disappointed with the last-minute cancellation.
Stephen Nelson said the stage was set-up for the band when the news was announced to the audience.
"They had set up everything, all the gear, their background was up, their roadies were on stage.
"Then 10 minutes before an announcement came on the PA that the gig was cancelled.
"People were like, 'are you serious?' Then the announcement was repeated and there was some booing."
Kathryn McKeown said the crowd were "disappointed" when the announcement was made.
"It was lashing rain on and off, everyone was drenched. Blossoms (the support band) were saying, 'are you excited for Kasabian?' before they finished.
She added: "About 10 minutes before the band were due on stage there was an announcement to say that due to last-minute illness the band would be unable to perform, tickets would be valid for a re-scheduled show.
"At first, I think everyone thought it was a joke. After about the third announcement it started to sink in and everyone started booing, some people were even chucking pints and plastic cups at the stage."
In a statement, organisers said: "Due to a last-minute illness we regret that the band have had to cancel tonight's show.
"We are working at this minute on scheduling a new date for Belfast. We will communicate with all ticket buyers via Ticketmaster and on the Custom House Square social media.
"Tickets will remain valid for the new date. We apologise for any inconvenience caused."
The band were due to play as part of a series of concerts at Custom House Square.

The rapper and songwriter said she would never condone Nazism in her art.
She added that both the producer and the person in charge of the video "happen to be Jewish".
The video also features rapper Drake, who is half Jewish.
Minaj said the video had not been influenced by Adolf Hitler's party but by a cartoon called Metalocalypse and also by Sin City, the comic book that was made into a film.
The director Jeff Osborne has been retweeting both positive and negative reviews of the video.
Her apology came after Anti-Defamation League, one of the top civil rights agency in the US said the video used "Third Reich imagery".
They argued the video was "a trivialization of the history of that era".
In the video Nicki Minaj is portrayed wearing a black body suit with stylised black letters on her chest. Some fans said this resembled a swastika.
Long red banners bearing the logo hang above her as she sits at the end of a corridor of tanks.
Guns fade across the screen as a drawing of Chris Brown in an authoritarian uniform flashes up, the logo emblazoned on his cap.
Troops in futuristic outfits are also drawn into the video, as well as grim reapers, futuristic flashing gas masks and storm trooper-type characters who appear to fan Minaj.  The ADL welcomed her apology, adding "We hope that she will take further steps to educate herself and her fans about who the Nazis were and why we should never take genocide or the Holocaust lightly."
Her full Twitter comments can be seen below.
Rock band Kasabian have cancelled a concert in Belfast minutes before they were due to take to the stage on Tuesday night.
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Nicki Minaj has apologised after the lyric video for her 'Only' track was accused of containing Nazi imagery.