Mr Ruto and the intelligence community have not commented on his allegations.
According to a state-funded human rights group, at least 80 people, including the minister’s son, have been abducted over the past six months.
The wave of kidnappings began after protests against tax increases last June and has continued ever since.
Some of the abductees were released under public pressure.
Earlier this week, the minister told reporters that he had received no answers about his son’s abduction, despite reaching out to higher-ups.
Muturi said the Directorate of Criminal Investigations (DCI) subsequently urged him to record a statement with them, saying the matter was still under investigation.
In his statement to the DCI, Muturi recalled that he called the Inspector General of Police, the Home Secretary, the DCI chief, the head of the intelligence agency and other top officials as he desperately searched for his son – but, he added, all were unable to help.
He said he also sent a message to Ruto but later decided to visit his official residence to raise the matter directly with him.
“I then recounted the ordeal (to the president), including my interactions with various high-ranking government officials who were unable to help. I expressed my belief that the NIS is holding my son,” Muturi said in a statement.
According to him, the president joked about this topic, and then called the head of the special service, who promised to release his son in an hour.
“I heard the president ask (NIS director) Noordin Haji if he is holding my son. (He) confirmed that he is indeed holding my son and the president instructed him to release Leslie immediately,” Muturi added.
Muturi has faced calls from some government allies to resign for publicly criticizing the government he serves.
Foreign nationals have also been abducted, including prominent Tanzanian activist Maria Sarungi Tsehai, who on Monday described how she was abducted by gunmen and released hours later.
Last year, Ugandan opposition leader Keiza Besigye was abducted in the Kenyan capital, Nairobi, allegedly by Ugandan security forces, and taken across the border to be tried by a military court.
Mutura’s public mention of Ruto’s name in connection with the kidnappings is a challenge to the president and is seen as contradicting the principle of collective responsibility in government.
It has also fueled speculation of defeats within the government, with other ministers and officials often denying that the abductions are being carried out by the state.
Amid public outrage, the president declared late last year that “we will stop kidnappings,” advising parents to instill good values in their children.
He also warned young people not to use social media to disrespect leaders amid continued widespread criticism of the government online.
