The facility would prevent jihadists from spreading their extremist ideology to the rest of society, he said.
The country's anti-terror law allows security forces to detain people suspected of terrorist activities for a long period without charge.
Kenya is battling home-grown militants linked to Islamist group al-Shabab, which is part of al-Qaeda.
In 2011, Kenyan troops entered neighbouring Somalia in an effort to stop the jihadists from carrying cross border attacks and kidnapping people.
Speaking at the passing-out parade of more than 2,000 prison wardens, Mr Kenyatta said additional money would be provided to meet logistical and operational requirements of the prison service.
The country's correctional facilities have previously been described as inhumane, with some of them heavily overpopulated, reports the BBC's Emmanuel Igunza from the capital, Nairobi.
At the moment, only death row inmates are kept in separate prison blocks from the rest of the convicts, he says.
It is not clear when and where the new prison will be set up.
Kenya contributes more than 4,000 troops to the 22,000-strong African Union force that is in Somalia helping the UN-backed government battle al-Shabab.
Al-Shabab has staged numerous attacks in Kenya. It killed 147 people at Garissa University, near the border with Somalia, on 2 April 2015.
It killed 68 people when it attacked Nairobi's Westgate shopping centre in 2013.
There are also regular gun and grenade attacks attributed to the group both in border areas, where many Kenyans are ethnic Somalis, and in Nairobi.
Al-Shabab has also set up a recruiting network in Kenya, especially around the port city of Mombasa, which has a large Muslim population.