Inspector General of Police Joseph Boinnet told Capital FM News that two of them have similar cases pending in court.
The order to have the suspects investigated was issued Saturday by Interior Cabinet Secretary Joseph Nkaissery who warned against gory images on social media in support of Al Shabaab.
Authorities are particularly concerned at images coming out of Somalia after the attack on a Kenya Defence Forces (KDF) base that left casualties on both sides.
“We have noted with great concern that there are unpatriotic characters who are still keen on amplifying the terrorist agenda through sharing of photos and sympathizing with the terrorists in such times of our nation’s loss,” Nkaissery said on Saturday.
This comes as four wounded KDF soldiers arrived in Nairobi from Somalia, where the Al Shabaab attacked the AMISON base during the early hours of Friday.
This is not the first time the Internal Cabinet Secretary has issued such orders.
In November 2015, journalist John Ngirachu was arrested after reporting on procurement by the Interior Ministry.
At the time, Nkaissery told a press conference that Ngirachu would be released after revealing the source of the information he had used to write his story.
Other cases include that of controversial blogger Robert Alai who was arrested last year over remarks he made on social media.