A hospital trust spokeswoman said the nurse's "child was doing very well" but could give no further information.
Ms Agyapong was admitted to hospital on 7 April, having tested positive for Covid-19 two days previously.
David Carter, chief executive of Bedfordshire Hospitals NHS Foundation Trust, said she was a "fantastic nurse and a great example of what we stand for in this trust".
"Our thoughts and deepest condolences are with Mary's family and friends at this sad time," he said.
Ms Agyapong's husband is currently self-isolating and has been tested for Covid-19.
Colleagues have paid tribute to Ms Agyapong, who also went by her married name Mary Boateng, on a fundraising page set up to support her family.
The page has already raised almost £4,500 since it was set up on Wednesday morning.
One former colleague said Ms Agyapong had "devoted her life to the NHS as a nurse".
Renai Mcinerney wrote: "Sister Mary was my colleague, I worked alongside her for a few years.
"She deserves her family to be looked after, after she devoted her life to the NHS as a nurse.
"It's time to look out/after our own and return the selflessness persona Mary carried and give something so small, but so big to her family in this time of need. RIP sister Mary!"
Caitlin Green posted: "So sorry to Mary's family and friends for her loss." SHARE THIS NEWS USING ANY OF THE BUTTON BELOW PLACE YOUR TEXT ADVERT BELOW ⬇⬇⬇