City Hall spokesperson Jason Post said the administration for children's services, a child welfare agency, took temporary custody of the diplomat's son and a daughter pending the outcome of an investigation.
He denied reports that the city was seeking a waiver of diplomatic immunity so authorities could charge the father.
Post said that at a meeting on Monday, the family, the city and Kenyan officials agreed "to continue to work to ensure the safety and well-being of the children".
Police department spokesperson Paul Browne said the diplomat, Fred Matwanga, 38, was taken into police custody on Saturday by officers responding to reports that he had assaulted his son.
He was released after police discovered he had a United States department of state-issued credential identifying him as a diplomat.
An ACS spokesperson, Sharman Stein, refused to discuss the case.
A woman who answered the telephone at the Kenyan mission to the United Nations on Monday said Matwanga was not at work. A home telephone listed for a Fred Matwanga in New York City rang unanswered.