The family of Nigerian novelist Chimamanda Ngozi Adichie has accused a hospital of negligence over the death of her 21-month-old son.

Nkanu Nnamdi died at a hospital in Nigeria on Wednesday following a short illness, leaving the family of the acclaimed postcolonial feminist writer "devastated".

Now, the family allege there was a litany of failures at Euracare Hospital in Lagos that led to the toddler's death, including being denied oxygen and being given too much sedation, causing a heart attack.

The hospital expressed its "deepest sympathies" over the loss of the child but denied improper care, which it said had been in line with international standards.

It added that Nkanu had arrived at the hospital "critically ill" and that an investigation into the death was now under way.