Kidero on Saturday said the seven day suspension will give affected tenants ample time to seek alternative accommodation.
He announced that demolition resumes next Saturday.
The demolition order was issued following the collapse of a building in Huruma where 45 people were killed as the search and rescue efforts entered its ninth day.
Dozens of Huruma residents on Friday spent the night in the cold as the government started demolition exercise.
People who had been living in the buildings began the search for new shelter carrying their furniture and possessions through the nearby streets.
The demolitions came a day after four people were pulled alive from the rubble of the building that collapsed last Friday last week when heavy rains hit Nairobi causing floods and landslides, although one died shortly after being rescued.