The property damage was reported at about 2pm on Thursday at the Nipperville Early Learning Centre, but a spokesperson for ACT Policing said staff had told them the first arrow had been found on Monday morning.

They were believed to have been shot at the building some time between Friday night and Monday morning.

The spokeswoman said it had been shot into one of the walls of the Nipperville building.

She said the second arrow, which was shot closer to the roof, was only noticed on Thursday, at which point the matter was reported to police.

The spokeswoman said there was no way of knowing exactly when the arrows had been shot into the childcare centre's wall but it was likely it had occurred over the weekend.

In a letter sent to parents, the Nipperville Early Learning Centre said police were notified as a precaution and police removed the arrows on Monday afternoon.

"The police believe it was a random act by youths and was not a targetted attack on our centre," said centre management.

"We will continue to be vigilant in our safety checks and report any further concerns immediately to the police."

The incident comes three months after eight police officers searched an employee and a minibus at the Nipperville centre.

The spokeswoman said there had been a case of property damage at the centre earlier in 2014.

It is understood the damage to the centre included graffiti although the centre was not specifically targeted with graffiti reported elsewhere in the area.