Spanish official David Fernandez Borbalan ruled out a late Shane Duffy winner and waved away penalty appeals.
West Brom's McClean described the referee as "Austria's 12th man" while O'Neill said the Spanish official was "very poor" in the Aviva Stadium game.
Fifa has begun disciplinary processes.
A Fifa spokesman told the BBC they are probing remarks made by both men and it is understood manager and player have until Friday to respond to the charges.
As well as ruling out Duffy's header, Borbalan also decided against giving the Republic a penalty when Jon Walters went down under a challenge from Stefan Lainer.
"It should count, the referee should have given the goal," the manager said of Duffy's header.
"I personally think it typified the referee's performance.
"The lineman thinks he has given a goal and he's almost up at the halfway line before he is called back."
The Football Association of Ireland declined to make any comment when contacted on Wednesday.
Fifa stated: "We can confirm that disciplinary proceedings have been opened.
"Be informed that two cases were opened: one against James McClean and another one against the coach Martin O'Neill."
A spokesman for the world governing body said there will be no further comment as the matter is ongoing.
Republic of Ireland boss Martin O'Neill and winger James McClean face punishment from Fifa for criticising the referee after the 1-1 draw in their World Cup qualifier with Austria.