The incident occurred at around 8:30 on Tuesday morning. A suspected perpetrator fled from the bus and is now being pursued by the police.
The police do not want to confirm that it is a knife, but tell TT that it is a sharp object.
There was no danger to other passengers, and the act is said to have been directed against the person who was taken to hospital.
There was no danger to more people, as far as I've been told, says Angelica Forsberg, press spokesperson for the Öst police region.
According to initial reports, the person is not critically injured. The incident is classified as aggravated assault.
Several police patrols are on site in central Jönköping.
The police do not want to give any details about the gender or age of the victim or suspected perpetrator.
It's far too early. We want to wait with details to see if we can gather witness statements that can lead to an arrest, says Angelica Forsberg.