Officials with METRO said the incident happened at around 9 p.m. at the Greenspoint Transit Center.
According to preliminary information, the customer boarded the bus, made physical contact with the operator, which led to a fight breaking out and spilling onto the street.
Officials said at one point, the bus operator got a sharp object and stabbed the customer.
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The person was taken to the hospital, where they're reported to be OK, METRO officials confirm.
It is unclear whether the two were familiar with each other or what caused the fight.
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The bus operator was detained at the scene, and METRO said it is fully cooperating with law enforcement as the investigation continues.