Mary Agyeiwaa Agyapong, 28, who worked as a nurse on a general ward at the Bedfordshire hospital for five years, died on Easter Sunday.
Her baby girl – also thought to be called Mary – was successfully delivered after an emergency caesarean section and is doing well, according to the hospital.
It is not clear if the newborn has tested positive for Covid-19.
ITV News understands that Ms Agyeiwaa Agyapong had been on maternity leave before being admitted to hospital.
It is understood that Ms Agyeiwaa Agyapong’s father has also died after contracting coronavirus, just days before his daughter.
In a statement on a fundraising page set up in her honour, friends and family of the 28-year-old described her as “a blessing to everyone she came across”.
The statement added: “Her love, care and sincerity will be irreplaceable.”
The Bedfordshire Hospitals NHS Foundation Trust said that Ms Agyapong tested positive on April 5 and was admitted to the hospital she worked at on April 7.
The hospital paid tribute to Ms Agyeiwaa Agyapong, who had worked on a general ward there for five years, saying she was “highly valued and loved” by her colleagues.
A statement from the Bedfordshire Hospitals NHS Foundation Trust described Ms Agyeiwaa Agyapong as a “loved member” of staff.
David Carter, CEO at the Trust, said in a statement: “It is with great sadness that I can confirm the death of one of our nurses, Mary Agyeiwaa Agyapong, who passed away on Sunday 12th April.
“Mary worked here for five years and was a highly valued and loved member of our team, a fantastic nurse and a great example of what we stand for in this Trust.
“She tested positive for Covid-19 after being tested on 5th of April and was admitted to the hospital on the 7th April.
“Our thoughts and deepest condolences are with Mary’s family and friends at this sad time. We ask that the family’s privacy is respected at this time.”