Ten-month-old Georgia Hollick choked on a piece of apple at Just Learning nursery in Cambourne, Cambridgeshire, last Wednesday. She was rushed by ambulance to Addenbrooke's Hospital but was later pronounced dead.
Ofsted has suspended registration at the nursery pending an investigation by Cambridgeshire police.
Jonathan Bell, operations director at Just Learning, said, 'This was a tragic accident and all our thoughts are with Georgia's family. The staff did everything they could for Georgia before the doctor and emergency services arrived and are deeply upset. We are co-operating fully with the inquiry.'
Chief executive Michael Fallon said, 'Last week's tragedy has been devastating for Georgia's family and has left everyone extremely shocked, sad and deeply upset.'
The nursery will be closed for several weeks while an investigation takes place.
Mr Fallon said, 'Staff are being offered counselling and we have contacted the parents of the other children to make them aware of alternative provision within our group and of the council number for childcare advice.
'It is too soon to reach conclusions about the circumstances of this tragic accident but we have full confidence in the police, Ofsted and the Health and Safety Executive to conduct thorough inquiries that will set out the facts and enable nursery operators to learn from last week's terrible event.'
Private sector providers offered their condolences. Alan Bentley, chief executive officer of The Childcare Corporation, said, 'While what happened at Cambourne must be thoroughly investigated, our hearts reach out to all involved. We should never lose sight of the fact that it is safer for children to be within a quality day nursery environment than in any other care system.'