In the 24th minute of the Sky Blues' 2-1 win over City on Sunday, Grant lunged into Atkinson with a tackle that caught the City defender on the shin.
He initially only received a yellow card but following a VAR review, the card was upgraded to red.
The MRP determined Grant committed the offence of "serious foul play" and offered the defender a three-match ban, with two games on top of the minimum one-game ban for a straight red card.
As things stand, Grant will miss Sydney FC's games against Adelaide United, Newcastle Jets and Melbourne Victory through suspension.
Sydney FC confirmed on Monday night they would appeal Grant's suspension.
"We will be appealing the decision of the independent match review panel on the basis of fact and comparative tackles that have gone unpunished," Sydney FC said in a statement.
"In addition, we would seek consideration for Rhyan Grant's exemplary disciplinary record for both club and country.
"Rhyan has amassed close to 250 senior matches, largely as a defender, and has never received a red card."