Relatives say Joseph only wants to come to the UK to donate bone marrow to his sister in order to save her life and then go back home.
Blood cancer charity The Anthony Nolan Trust and the African Caribbean Leukaemia Trust (ACLT) have now launched a campaign to overturn the decision.
Shirley has been receiving treatment at Birmingham’s Queen Elizabeth Hospital but doctors fear she is now running out of time.
Shirley, of Walsall, West Midlands, who is mum to four-year-old son Blessing, said: “My life is in danger – I need to get my life back for my son.
“I have my little boy, and I want to live for him.”
Shirley is entirely reliant on blood transfusions to reduce her life-threatening anaemia, and her reduced white blood cells put her at high risk of infection.
A “Grant This Visa To Save A Mum’s Life” petition created three days ago urging the government to reverse its decision has already amassed over 41,000 signatures.
The Anthony Nolan Trust said there are no other options for a donor on the international stem cell register, and no way for Joseph to donate in Ghana.
Spokeswoman Elana McIntrye said: “There are no alternative donors in the UK, or worldwide.
“When a patient needs a match Anthony Nolan searches the UK and international registers to see if there are any suitable donors.
“Joseph is a 10/10 match. As there are no other donors, he is Shirley’s only option.”
Henny Braund, Chief Executive of Anthony Nolan, said the Home Office had made concessions for similar cases in the past.
He said: “Shirley’s best chance of recovery so she can care for her young son, Blessing, is a stem cell transplant and I am deeply concerned her bother Joseph, who is a perfect match, has been denied a visa.
“The Home Office has made concessions for similar cases in the past and I urge the Minister to reconsider.
“Each passing day leaves Shirley increasingly anxious, and at increased risk of infection.
“His sister is in need and Joseph is ready – the situation needs to be urgently resolved so Shirley can have the treatment she so desperately needs.”
Orin Lewis, Chief Executive of the ACLT said: “The stark reality is Shirley has no other option. The search for an unrelated donor is made difficult due to her African heritage, which means she is three times less likely to find a perfect match.
“The Minister needs to step in and give Shirley her best chance of life, and raising her young son.”
A Home Office spokesperson confirmed they are reviewing the decision.
A statement said: “We are urgently reviewing the decision and will give very careful consideration to the compassionate circumstances.”
In a previous letter to Shirley, the Home Office said: “While I am aware of the importance of family contact and the compassionate nature of your application, I must, however, also consider your personal and financial circumstances in Ghana when addressing your application.”
By Ben Gelblum and Faith Ridler
