The Celtic defender's case was due to be heard by an appeal tribunal last Thursday.
By submitting the appeal against the dismissal for denying Peter Pawlett a clear goal-scoring opportunity during the game at Pittodrie on Feburary 25, Van Dijk's automatic one-game ban was put on hold.
That meant he was available to line up against Inverness Caley Thistle a week past on Saturday.
Manager Neil Lennon insisted the reason they had appealed the red card, shown by ref Craig Thomson after just 12 minutes of the 2-1 defeat to the Dons, was because they felt they had a very good case.
He was adamant that it was not a clear goal-scoring opportunity because Pawlett was moving away from goal and Efe Ambrose was getting back to cover.
Lennon explained: "We are appealing because we think it is worthy of an appeal.
"We will see what the outcome will be. You just never know with these things.
"It's not like we are wasting anybody's time on it. We feel we have a decent case."
However, the SFA have confirmed the appeal was withdrawn before it was due to be heard at Hampden last week.
The £1,000 appeal fee was forfeited, and Van Dijk will now miss Celtic's next match, at Rugby Park on Friday night.
By the time the Dutchman is available to play again, in the home game against St Mirren a week on Saturday, he will have been out of competitive action for three weeks.
However, while Van Dijk is out of action, he is not being kept out of the news.
His agent, Henk-Maarten Chin, revealed he expects the 22-year-old - who cost £2.6million when signed from Groningen in June - to move to one of England's top clubs when the transfer window reopens.
He said: "I expect something will happen for him this summer. The intention would be for him to earn a top transfer."
The defender added fuel to the speculation his stay at Celtic may be for only one season when he tweeted a picture of himself alongside Chelsea's David Luiz with the comment: "Last night dinner @DavidLuiz-4".
Nir Biton is another Celtic player who is about to spend time on the sidelines.
The midfielder sustained a groin injury while playing for Israel in a friendly international against Slovakia last week.
The medical team at Celtic are now assessing the extent of the damage.
But it appears the 22-year-old - who watched his previous club, Ashdod FC, play Hapoel Tel Aviv on Saturday - could miss Celtic's final 10 games of the campaign.
Lennon and his staff will also assess the condition of the other 12 first-team players who were away on international duty now that everyone is back at Lennoxtown following a well-earned few days off.