The incident happened Wednesday morning around 9 a.m. on Grand Concourse and East 138th Street.
Police say it all started with a verbal dispute between the 52-year-old bus driver, Ernesto Hernandez, and 50-year-old Alejandro Noboa.
Hernandez is accused of punching Noboa in the face, causing a bloody nose.
Noboa is accused of punching Hernandez and causing a laceration to his lip and left temple.
It is not yet clear how the incident unfolded.
Both men were arrested and charged with assault and harassment.
MTA's Aaron Donovan released the following statement:
"The bus operator in question is currently being held out of service as we review and determine the facts."
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