The incident happened during the third quarter of Friday night's pre-season game.
Fans sitting near the Hawthorn supporter alerted authorities and he was escorted from the stadium within minutes, the league's website reported.
The fan also has a young boy with him.
It's not known if the abuse was racial.
Two fans were evicted for racially abusing Daw during an AFL game between North and Western Bulldogs at Etihad Stadium in 2013.
The ruck/forward was also taunted by a Hawthorn fan last year and in 2011 a Port Melbourne supporter was evicted from North Port Oval for racial abuse.
The Hawks immediately launched an investigation into the incident.
"Hawthorn FC is investigating if a man escorted from Aurora Stadium tonight for racially abusing Majak Daw is a club member," chief executive Stuart Fox said.
"We would remind all members, supporters and footy fans that Hawthorn Football Club has a zero tolerance approach towards anyone who racially vilifies a player, official or patron.
"Racial vilification at the football in any form is offensive and totally unacceptable -- not just to the target of the vilification, but also to all players and supporters."