They had been due to play the first of three gigs at the SSE Arena on Tuesday, reported BBC News.
The cancellation announcement was made at about 9 pm, when most of the audience was already inside the venue.
Disappointed fans booed as staff instructed them to leave the venue and one witness said "hundreds" of girls and women had been left weeping.
Concert promoter Aiken PR said: "The show tonight has been cancelled as Liam has taken ill, and whilst not serious, he is unable to perform tonight."
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In a statement, the band, who are undergoing a final tour before taking their first break next year since forming on X Factor in 2010, apologised to their fans.
And on his Twitter account, Harry Styles wrote: "Deepest apologies to everyone at the show tonight in Belfast. Very disappointed, but unfortunately these things happen. We're very sorry."
Band mate Louis Tomlinson tweeted: "We're so so sorry for what happened tonight, it was out of our control! Lots of love to Liam and thank you for being so understanding!"