The patient, in her 80s, had underlying health conditions and passed away on March 12 but her death was only confirmed on Tuesday.
The woman was being cared for at Walsall Manor Hospital and became the first confirmed person to die in the borough after testing positive for Covid-19.
Richard Beeken, chief executive for Walsall Healthcare NHS Trust, said: "Sadly, we can confirm that a woman who was being cared for at Walsall Manor Hospital and tested positive for Covid-19, has died.
"The patient, who died on March 12, was in her 80s and had underlying health conditions.
"Her family has been informed and our thoughts and condolences are with them at this difficult and distressing time."