In a statement, Greens co-leader James Shaw said Davidson was seeing a doctor after the incident and had reported it to police.
Media have variously reported that the incident occurred before and after the protest.
Davidson attended today's rally to support trans and non-binary human rights and was injured by the motorcyclist after Parker left Albert Park under a police escort.
A large number of motorcyclists were in the area to support another rally held by Brian Tamaki.
Shaw said the news Davidson had been injured was upsetting and "we are asking people to show care and love".
"We ask everyone to give Marama and her whānau some space and time to process what has happened."
Shaw said the Green Party stood with its trans and non-binary whānau.
"Aotearoa should be a place where everyone can live their lives without fear of hate or discrimination."
