The star was due to perform for crowds at Birmingham Pride this weekend, which comes less than a month after Sarah died from breast cancer at the age of 39.
Cheryl explained that she is not “emotionally, mentally or physically able to perform”, admitting her heart is ’heavy”.
In a statement posted on her Instagram Story, the singer wrote: “Saying goodbye to somebody you spent such a massive piece of your life with is like nothing else.
“My heart is heavy. Grief is such a harsh experience and an absolute rollercoaster of emotions. Questions without answers and pain without resolve. So tumultuous and constant.
“With that said I am so sorry but I really am not emotionally, mentally or physically able to perform for you this Saturday at Birmingham Pride.”
Cheryl continued: “I apologise wholeheartedly and I can only hope for your understanding (I promise I will make it up to you somehow).
“I feel now I just need some time to sit with my feelings and process the grief…
“Nothing prepares you for this bit,” she added with a broken heart emoji.
Sarah died on 5 September after being diagnosed with stage four breast cancer last year.
In the days after her death, Cheryl, Kimberley Walsh, Nicola Roberts and Nadine Coyle all paid heartfelt tribute to their late bandmate on social media.
At the time, Cheryl described Sarah as “stunning, unique, crazy, quirky, kind and soft hearted” as she admitted she was “at a loss for words”.