The person, whose identity has not been disclosed, has since been released on bail with conditions until 9 August.
It follows the permanent closure of the 39-place nursery last month after it received an inadequate Ofsted inspection grade in April.
According to the Ofsted report, the setting’s arrangements for safeguarding were ‘not effective’.
It highlighted that ‘frequently, the provider and staff do not offer any comfort or reassurance or acknowledge children when they are upset and crying.’
Inspectors also found partnerships with parents were not effective, children’s personal, social and emotional development were not prioritised well enough and children did not receive high-quality interactions from staff.
Grafton Childcare was established in 1991 by owner and manager Denise Tupman.
A spokesperson for Devon and Cornwall Police said, ‘The Police and partner agencies are investigating allegations that relate to safeguarding concerns at Grafton Childcare, Newton Abbot.
‘One person has been arrested in connection to this matter and has since been released on bail with conditions until Wednesday 9 August.
‘Anyone with any information, or has concerns over this message is asked to contact 101 quoting case reference 50230124535.’