The police received an anonymous call to report concerns.
The woman is thought to have been drunk in charge of her young child and also allegedly dropped the child on the ground in the street
Officers visited her home and arrested her on suspicion of being drunk in charge of a child just before 4am. This was after a short chase on foot where she jumped fences of nearby gardens.
The child is now being cared for in a safe environment.
Cambridgeshire police says: “Do you have similar concerns? Remember sharing any worries with us, no matter how small or insignificant they may seem, could make a huge difference to a child’s life.
“You don't have to be sure. Find out more here.”