Rajeshwariben, as she was known, was 65 and died while undergoing treatment at a private hospital in Mumbai, after a recent lung transplant at Ahmedabad hospital.
The doctors in Ahmedabad later referred to a hospital here.
Shah had visited her at the HN Reliance Foundation Hospital in south Mumbai last week and Chief Minister Eknath Shinde and Industrialist Mukesh Ambani had called on her.
Following her demise, Shah has cancelled all his public engagements and is likely to take part in her funeral in a suburban locality in Ahmedabad, the details of which are not immediately known.