The President was accompanied by Nairobi Women Representative Rachel Shebesh, Deputy Governor Jonathan Mueke, Dagoretti South MP Dennis Waweru and Inspector General of Police Joseph Boinnet.
County officials said seven people have been confirmed dead and that the number could rise as search and rescue efforts continue.
More than 133 people have so far been rescued from the rubble.
Kenya Defence Forces have been deployed to assist in rescue operations.
Mr Mueke ordered people residing in adjacent buildings to evacuate immediately to avoid a similar disaster.
According to the National Disaster Operations Centre officials, people are still trapped in the building as voices can be heard in the rubble.
The six-storey building had 198 rooms.
Kenya Red Cross on Saturday said at least 1,000 people have been displaced in Mathare and Mukuru slums following heavy rains that pounded Nairobi on Friday.
“Approximately 800 households (were) affected in Mukuru Kayaba, Land Mawe, Kinyago last evening (Friday),” the humanitarian organisation added.