Officers said the suspect was taken to the camp by the public who spotted her with the baby in a residential block in the area sprawling suburb.
The two-week-old twin boy was stolen at Kenyatta National Hospital’s waiting area.
The mother of the twins, Jane Kerubo, who delivered at the county’s top referral hospital two weeks ago, had been taken to the facility on Sunday 2am with breathing difficulties.
CCTV cameras at the hospital captured a woman holding a baby, believed to be the stolen newborn, moments before she boarded a motorbike and sped off.
It is believed that Mr Ouko and his wife warmed up to the two strangers as they spoke in their local dialect.
“Ms Naomi Leo (Jane’s sister) requested the ladies to hold the babies for her while she assists her brother-in-law to wheel her sister to the ward,” the hospital’s communications manager Simon Ithai explained in a statement.
“Shortly after they entered the ward, one of the ladies who had one of the babies by the name Lucy Kwamboka, came to the ward claiming that the other lady had disappeared with the other baby and they needed to raise the alarm,” Mr Ithai added.
The newborn was returned to KNH for medical examination.