The club announced the punishment on Tuesday, with McDonald also apologising for his "naive" and "disrespectful" behaviour.
Former Dundee midfielder McDonald, 21, was substituted at the break with Burnley 5-0 down.
He said: "I now realise it was naive, disrespectful and totally wrong of me to leave the ground at half-time on Saturday.
"It was a gross misjudgement and instead I should have remained at Turf Moor to support my club and team-mates.
"I acknowledge that I also showed a serious lack of respect to all the fans who were at the ground and who pay good money to watch their team play.
"I would like to apologise to the players, management and supporters and I have accepted my punishment.
"In closing, I would like to reassure all supporters that I am fully committed to helping the team as we fight to stay in the Premier League."