In a post on its official X page, the authority condemned the behavior as totally "irresponsible and reckless".
"Unacceptable Behavior!," it wrote.
The footage, captured in an undisclosed location, shows the 14-seater matatu swerving dangerously from side to side on the road.
Passengers are also heard blowing whistles an act akin to cheering on the reckless driver oblivious of the dangers that might befall them.
Some of the crew are also seen peeping through the windows from both sides.
"The driver risked his life, that of his passengers and other road users. In a split second, a catastrophic incident could occur as a result of such behavior," the authority said.
The post has since attracted mixed reactions from X users.
"The work of enforcement is to arrest and punish such characters. I don't want to hear anyone shifting responsibility to the general public for whatever they are not doing, failure to uphold road rules is misconduct and we must be protected by all means possible that's the meaning of laws," J.Otao wrote.
Rule number 80 of the Traffic Act states that anyone found travelling with part of the body outside a moving vehicle is liable for a fine of Sh1,000.
Section 53(1) and 67 states that a motor vehicle that obstructs by allowing a vehicle to remain in any position on the road to obstruct or cause inconvenience to other motorists using the road is fined Sh10,000.
"Hawa watu washikwe woote and their licenses revoked. I once met with them along thika road and trust me it was bad," said Muchiri wa Kinyua.
NTSA had on Sunday arrested excess passengers aboard public service vehicles in Thika, Kiambu.
In a post on X, NTSA said motorists should avoid boarding overloaded vehicles to prevent inconveniences.
“To avoid any inconveniences, do not board an overloaded vehicle,” the transport and safety authority said on X.
Vehicles without proper documents including inspection and road service license (RSL) were also impounded.
NTSA's principal communication officer Anthony Nyongesa said the crackdown was a routine exercise that is taking place across the country.
The transport authority and the police have recently intensified a crackdown against traffic offenders, following an increased number of road accidents across the country.
