The 23-year-old was sent off by Miller towards the end of Saturday's 1-0 defeat at Bolton.
The reason for the red card was initially unclear but video footage filmed from the stands has since emerged which seems to show Barnes sticking out his leg as the official ran past.
Barnes has already been hit with an automatic four-match suspension, which includes an additional match for his second red card of the season, but he could be facing an even longer ban.
The FA also confirmed it is considering taking action against Crystal Palace winger Wilfried Zaha after he was photographed appearing to make an offensive gesture towards Leeds fans during Saturday's 2-2 draw at Selhurst Park.
The 20-year-old, who in January agreed a move to Leeds' traditional rivals Manchester United, later apologised for his actions on Twitter.
He wrote: "I...wanted to apologise for the gesture I did towards the Leeds fans in yesterday's game. Very unprofessional from me."