In a letter seen by the Catholic Herald, the Home Office said she had not given enough information after her finances.
She had hoped to visit her sick sister, but despite previously travelling to the UK she's been told she cannot appeal.
Sister Ban was recently displaced from her home in Qaraqosh after fleeing Islamic State.
It's reported she now lives in Erbil where she has set up kindergartens.
It's not the first time religious figures have been denied entry to the UK. In December 2016, three archbishops from Iraq and Syria were denied visas to enter the United Kingdom because the Home Office thought they were too poor because she did not have a personal bank account because she belonged to a religious order.
In December 2016, three archbishops from Iraq and Syria were refused entry into the UK despite being invited by the country's Syriac Orthodox Church for the consecration of the UK's first Syriac Orthodox Cathedral, attended by Prince Charles.
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