The singer posted on Twitter to say that she had contracted laryngitis and had to postpone the show.
Refunds are being offered to disappointed fans, though the singer has said she hopes to re-schedule for another date.
The Wardrobe has issued a statement urging ticket holders to contact the place they bought the ticket from to request a refund.
Becky said on Twitter that she had completely lost her voice and was heading to London for tests.
She wrote: "I am so sorry to say I have contracted laryngitis and completely lost my voice and therefore I'm gonna have to postpone tonight's show in Leeds.
"I'm devastated to say the least. We've all worked really hard to make sure this tour is the best show you've seen and I'm gutted I won't be able to deliver the show you deserve.
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"I'm heading back to London now for a full ENT scope to see the extent of the damage but can't risk singing on an inflamed larynx as it could lead to vocal haemorrhage which would mean I'm properly in the **** and would have to take 12 weeks vocal rest and surgery.
"This is all very scary for me and now I have a horrible guilty feeling that I've let you all down.
"I just need to put my vocal chords first. I'm so sorry.
"The date is being rescheduled (more info asap) and refunds available."
The Leeds concert is the second which the singer has had to cancel in recent days after a burst water main forced her to call off her gig at the Manchester Academy on Wednesday night.
Despite the cancellation the singer performed an acoustic set in the street for around 200 fans who had turned up for the show.
Source : https://www.yorkshireeveningpost.co.uk/our-city/becky-hill-cancels-leeds-show-at-the-wardrobe-details-on-how-to-get-a-refund-1-9392565