Writing in a newspaper column, Boyd made reference to the fact that Celtic captain McGregor was wearing a protective mask during the 3-0 victory over Rangers on Wednesday night in his first match since since suffering a fractured cheekbone against Alloa in the Scottish Cup.
Boyd, who had two spells at the Ibrox club during his playing career, wrote in The Sun: “Look at Celtic. Callum McGregor played with a fractured cheekbone.
“The fact he managed to get through the 90 minutes without anyone testing out that face mask is another story, but his commitment to the team was tremendous.”
The comments have caused uproar among Celtic fans on social media and the club have responded confirming it is looking into the matter.
A Celtic statement read: "With regards to comments made by former professional footballer Kris Boyd concerning Callum McGregor's injury, we can confirm that the matter is currently being addressed by the club.”