The domestic incident unfolded on Victoria Road in Fenton, which was sealed off between the roundabout at the top of the road and Manor Street.
Trained police negotiators supported by Staffordshire Police and local neighbourhood officers at the scene.
Residents were warned to go into their houses and not come out until they were told it was safe.
The man, aged 29, and the child were arrested at 3.40pm today (November 16) and taken into custody for questioning.
It is unknown what the arrests were for. The road was reopened at around 4.30pm.
Police have now launched an official investigation into the incident.
A Staffordshire Police spokesman said: “Specially-trained police negotiators, supported by uniformed colleagues, worked to resolve the incident safely and local neighbourhood officers supported the operation by maintaining the cordon around the address.”
The spokesman added the man is now receiving support and treatment for a mental health condition.