Aloisi is accused of striking Adelaide assistant coach Jacobo Ramallo in the back while in the tunnel, exiting Coopers Stadium after the Roar's last-gasp loss to Adelaide United.
Ramallo is understood to have been felled by the blow, which happened minutes after Brisbane conceded a controversial penalty to lose the game 2-1.
Roar football director Moore was also cited under the FFA's national code of conduct over alleged comments made towards referee Steven Lucas after the match.
The pair have until 5pm (AEDT) on Wednesday to make submissions, and face anything from a reprimand to a fine and/or suspension.
Meanwhile, Brisbane goalkeeper Michael Theo was handed a two-match ban after the panel ruled he committed "assault on a player".
Theo was red-carded for elbowing Adelaide's Dylan McGowan in the 96th minute of the match, leading to Sergio Cirio's penalty that sparked the heated post-match row.
He has until midday on Tuesday to appeal.
It came after Adelaide defender McGowan called for Aloisi to face repercussions if found guilty, while stressing he didn't see the incident or personally know who was involved.
"We are trying to market the game here in Australia and all these sort of incidents bring negative light to the game which is unfortunate," McGowan said.
"I don't know who was involved so I can't be saying that they (FFA) need to come down on whatever it is.
"I'm sure that they're looking into it.
"And, to be honest, the Adelaide tunnel has got plenty of people in it so someone has seen it.
"And there will be hopefully repercussions if there was something done wrong. Hopefully there's repercussions for it because it was something we don't want to see in the game."
The Roar reiterated they will cooperate with FFA but refused to comment further.