"Police are able to reassure other parents that this appears to be an isolated incident and that they are not seeking anyone one else in relation to this."
Police thanked the community for information provided, which assisted in identifying the man.
The Ministry of Social Development (MSD) which runs the school holiday programme, and the Ministry of Education (MoE) have been informed of the incident and subsequent arrest.
In a statement, an MSD spokesperson said the ministry would be investigating the incident.
"The safety of children is a paramount consideration in children's holiday programmes.
"Our thoughts are with this child's family."
The ministry funded a range of holiday programmes delivered around the country each year.
MoE acting deputy secretary David Wales said it was "always distressing to hear about an incident like this".
"However it's pleasing to see that the staff running the holiday programme were vigilant and contacted the police immediately.
"In instances like this, it's really important that those working with children contact the police as soon as they observe any suspicious behaviour."
It was timely for families, whanau and caregivers to speak with children about staying safe, Cameron said.
This could include:
• Have sensible family safety guidelines.
• Have discussions around behaviours and actions that are inappropriate or that make them feel uncomfortable, rather than concentrating on the types of people who could harm them.
• Encourage children and young people to take action when they feel unsafe or uncomfortable.
• Make it easy for your child to talk to you and tell you about anything that is bothering them.
• Listen carefully to what your child is saying. They are unlikely to tell you directly about what is bothering them so you may need to read between the lines.
Advice for children:
• Remove yourself from the uncomfortable situation, no matter who is causing it.
• You must tell someone if other people make you feel unsafe, worried or scared.
• If the first person doesn't help, go on telling until someone listens and takes action.