Nineteen-year-old Chris McKee, who joined City on loan in March, was dismissed by referee Craig Napier 41 minutes into Sunday's 1-0 defeat by the Lowland League champions as they slipped out of Scottish League Two.
The BBC later reported that he had allegedly used foul and abusive language of a homophobic nature, and parent club Rangers moved swiftly to look into the matter.
An Ibrox spokesperson said: "Rangers are aware of an incident involving one of our on-loan academy players during a match this afternoon.
"We will investigate this incident thoroughly and it will be treated with the utmost seriousness. As a club, we oppose all forms of discrimination. We will handle this incident robustly."
Brechin, who went into the game trailing 2-1 from the first leg, ultimately lost 1-0 on the day and 3-1 on aggregate courtesy of Michael Tidser's 88th-minute strike, although by that point, the visitors too had been reduced to 10 men when Scott Hooper was sent off for a challenge on Rory Currie.