The ex-Scotland international, now an ambassador for the champions, accused the top-level official of a "pre-meditated decision" not to award Celtic a penalty in the closing stages of normal time during Celtic's extra-time win over Dunfermline in the Betfred Cup.
• READ MORE - Former Parkhead defender peddles anti-Celtic conspiracy on club TV during Dunfermline clashBoyd, co-commentating on Celtic TV, claimed Beaton shouldn't be taking charge of matches if he "doesn't know the rules" adding: "I’m not mystified. John Beaton... it’s obviously a pre-meditated decision not to give that penalty because it was so late in the game."
The Scottish FA compliance officer Clare Whyte is probing the comments and if she decides that Boyd has contravened Rule 38, 29.2 - "A club or recognised football body which publishes, distributes, issues, sells or authorises a third party to publish, distribute, issue or sell a match programme or any other publication or audio/visual material of any description in any media now existing or hereinafter invented, including but not limited to the Internet, social networking or micro-blogging sites, shall ensure that any such publications or audio/visual material does not contain any criticism of any match official calculated to indicate bias or incompetence on the part of such match official or to impinge upon his character" - the club could be hit with a hefty fine.
Clubs can face fines of between £1,000 and £100,000 if found to have breached the stringent rules.
Celtic said earlier this week that they were "astonished" at the investigation, saying in a statement: "We have had absolutely no contact from the SFA in relation to this matter and, given the context and circumstances in which the comments were made, would be astonished if the matter were to be progressed.
"If it is, then we will respond robustly."
Former Parkhead striker John Hartson has waded into the row, backing his former team-mate by commenting: "Been there, seen it, done it" on social media.