Television footage showed hundreds of people scaling a wall to gain access to the 60,000-seat Kasarani stadium in Nairobi, which was packed with spectators before dawn.
Dozens of people can be seen falling on top of each other in a crush at one entrance gate, while first aid responders carried people to a waiting ambulance.
The Kenyan Treasury Department has provided 200 million shillings or about $1.6 million (R27.3 million) for the inauguration ceremony. It will be less costly than Kenyatta’s 2017 inauguration, for which taxpayers paid over 300 million shillings
Police spokesperson Bruno Shioso said the stadium was filled to capacity at 5am (0200 GMT) and urged Kenyans to follow the proceedings from home.
In anticipation of being part of history, Kenyans have thronged to the venue in large numbers, Shioso said in a statement.
To avoid logistical challenges, this is to request the public to make alternative arrangements to view the proceedings, especially from the comfort of their homes.
By law, Ruto must take the oath of office by 2pm (1100 GMT) on Tuesday, five weeks to the day since the August 9 election that saw him clinch a narrow win over his rival Raila Odinga.