McGinn was summoned to an SFA disciplinary hearing after branding Beaton's display as "inept" and has been found to be in breach of rule 72, which states that any criticism of a match official should not “indicate bias or incompetence” or “which impinge on his character”.
McGinn’s remarks related to a free-kick that led to Celtic’s winning goal, scored by Kyogo Furuhashi, and the referee’s decision to allow it to be taken so quickly, with Hibs players apparently waiting on a substitution after they saw the fourth official with the board ready.
In the aftermath, a visibly livid McGinn said: "It's not a foul and then the fourth official is holding the board. I think Jamie Murphy could stand over the ball, as you do, but he steps away from it, to assume 'sub'.
"No control over the situation, [Beaton] he just lets it happen, and the goal goes in. I don't know if you see me running to him straight away and get myself booked. But it's just inept.
"Even 90 seconds later, Celtic are going to make a sub [there’s] a quick throw-in, and he whistles it back for the sub to happen.
"I ran to him and just said 'What's going on? There is no way we would have got that the other way. No way!’"
The right-back will now miss Hibs’ next two fixtures against Celtic on Monday, January 17 and Cove Rangers on Thursday, January 20.
Fellow defender Ryan Porteous is also suspended for the aforementioned fixtures as well as the match against Motherwell on Wednesday, January 26 after copping a three-match ban for kicking out at Aberdeen striker Christian Ramirez in a 1-0 win at Easter Road last month.
The asbence of two regular starters in defence could see Shaun Maloney hand debuts to new January window signings Harry Clarke and Rocky Bushiri.