The two separate incidents of reported violence on buses took place in the Loimaa municipality in western Finland and Uurainen, a municipality in the centre of the country, according to the NBI.
The NBI's Sanna Springare, who is lead investigator in the incidents, said the agency does not know whether the two incidents were related. The suspects allegedly involved in the incidents have foreign backgrounds and are in their 30s.
Springare said it is too early to say whether the incidents were related to terrorism, but they are looking into that possiblity.
The most recent incident took place at around 1:00 am on Wednesday in Uurainen, on a bus that was driving from Helsinki to the north-western city of Oulu.
The NBI said the man who caused the incident had suddenly gotten out of his seat on the bus and then attacked the driver.
Passengers who were sitting at the front of the bus near the driver saw the incident unfold, overpowered the man and wrestled him to the floor of the vehicle, according to the NBI.
The passengers then held the alleged attacker on the floor until a police unit arrived on the scene, the law enforcement agency said.
There were a reported 15 passengers aboard the bus at the time of the incident.
The NBI is investigating the incident as suspected attempted traffic endangerment and suspected petty assault.
Similar incident on Tuesday
Police are also investigating a similar incident that allegedly took place on a bus driving through south-west Finland on Tuesday afternoon.
That bus, which had five passengers, had just begun its journey from Loimaa towards Turku. A male passenger got up from his seat, walked to the driver and grabbed the steering wheel, turning the bus into the other lane according to police.
CEO of the bus company Petri Valtanen said the bus veered into the opposite lane and grazed the side of another bus travelling in the opposite direction. The driver of the other bus swerved out of the way, resulting in only the side mirrors of the buses being damaged.
"If the driver in the other bus hadn't reacted [so quickly] it would have been a head-on collision," Valtanen.
The driver of the bus with the alleged attacker in it stopped the vehicle at a nearby bus stop and managed to get the man outside with help from passengers and called police.
Edited on 7 December at 15:20 to reflect Tuesday's incident involved a bus driving from Loimaa towards Turku, not the other way around.