The Port Adelaide Power spectator aimed the banana at Adelaide Crows' Eddie Betts after he celebrated scoring a goal in the game at Adelaide's Oval.
Port Adelaide have banned her "indefinitely" after deciding her actions breached their code of conduct.
"It is clear that the offender's behaviour was racially motivated," said a club statement.
Footage on social media appeared to show the fan pick up the banana and throw it in the direction of Betts, before his team-mate Josh Jenkins intercepted it.
The woman will be invited to take part in Power's Aboriginal cultural awareness programmes, the club said.
The statement added that as part of this programme, "the club's seven Aboriginal players would educate her on cultural issues that continue to have an impact on the Aboriginal community today and the hurt which actions such as hers cause others."
A Crows statement from chief executive Andrew Fagan said: "There is no place in our game or society for such abhorrent behaviour."