Aliir had taken a mark on the goal line in the final quarter at the SCG before a Swans fan appeared to throw the object at him.
Former Sydney player Aliir then called out the spectator at the boundary fence before returning to the match, which the Power won by eight points.
The fan was subsequently interviewed by police and SCG staff, and was removed from the stadium.
Sunday's incident comes after star Port forward Willie Rioli endured online racial abuse following their upset win over Hawthorn in round five.
Rioli had shut down his social media accounts and took leave from the club after a now-deleted Instagram post regarding his family history with Hawthorn.
Hinkley confirmed Aliir was "OK" in the aftermath, while Sydney chief executive Tom Harley spoke to the player after the final siren.
"I don't know exactly what happened there, so I don't really want to comment on that," Hinkley said.
"As far as I know, there was something that went on.
"I think Aliir was OK with everything, so we'll work through it.
"Let's respect our footballers. That's the most important thing.
"We've had a little bit of a stuff go on over the journey, last few weeks particularly, and I think let them (players) do what they do.
"You come to watch them. Just admire them for what they are, I would have thought, and enjoy the game.
"If you can't do that, please don't come."
Sydney counterpart Dean Cox echoed Hinkley's sentiments.
"Anything (abusive) from fans, members, supporters to players or anyone involved in footy - we don't condone," Cox said.
"That's one thing that I stand firm on and so do the club."
Sydney, who have yet to ascertain if the fan is a member, reiterated in a club statement after the match their "zero-tolerance stance on all forms of abuse".
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