Tuesday’s action came after Mwai Kibaki, the Kenyan president, announced the resignation of his energy and education ministers on Monday.
George Saitoti, the education minister, was on the top of the list.
Saitoti, who was Moi’s vice president, has been implicated in Kenya’s biggest financial scandal, a fraud dating back to the early 1990s.
Gideon and Philip Moi, two sons of Daniel arap Moi, the former president, were also included.
The police also ordered the suspects not to leave the country without permission.
In the statement issued on Tuesday morning, police listed Saitoti and the other 19 men as suspects in that fraud, known as Goldenberg.
In an address on state-owned television on Monday, Kibaki said Saitoti and Kiraitu Murungi, the former energy minister, had left the government to allow for investigations into two separate scandals.
The resignations came as pressure mounted on Kibaki to respond to allegations of high-level government corruption made last month by John Githongo, who served as Kibaki’s anti-corruption ombudsman for two years until February 2005.
Kibaki won elections in 2002 promising to root out the corruption that had become endemic under Moi’s 24-year rule.
Police have ordered the suspects
Now, though, Kibaki is accused of allowing the old ways, and even some discredited figures from the previous government, to hold sway.
The scandal began as a ploy to get export credits for gold and diamond jewelry but evolved into a complex web of financial dealings.
Earlier this month, an inquiry report on the gold scandal recommended further investigation of the role of Moi, the former president, and pressing criminal charges against Saitoti.
The second scandal, named after a fictional company called Anglo Leasing, emerged in 2004 and implicated some of Kibaki’s closest confidants, namely the finance minister who resigned a week ago, Murungi, and Kibaki’s personal assistant Alfred Gitonga.