A 21-year-old woman has been taken into police custody after she allegedly assaulted a toddler at a Perth shopping centre.

The incident unfolded on Tuesday afternoon when a mother holding her child at the Park Centre in East Victoria Park was approached by a woman in a pink singlet.

CCTV vision of the incident released by police showed the woman rushing across to the mother, then reaching across and assaulting the child as the mother tried to turn her body away from the attacker.

The woman in the pink top then fled the scene.

Police said the toddler received facial injuries in the attack.

In a statement late on Wednesday morning, police said a woman was taken into custody at Mirrabooka Shopping Centre about 11:10am.

Police earlier named the alleged attacker as Pamila-Raye Jetta and said she was unknown to the mother.

Constable Imran Ishak told ABC Radio Perth finding Ms Jetta was a top priority due to the nature of the incident. 

But he warned she should not be approached.

"We have identified her through thorough investigative methods. We are putting all our efforts into locating her," Detective Ishak said.

"If members of the public do see her, we do want to remind members of the public to exercise caution and remain vigilant.

"We are just advising members of the public not to approach her."

Mr Ishak said the toddler was not seriously injured and both mother and child were receiving support.