Their hosts, on the other hand, have been permitted to field the Scotland A captain, Jonny Gray, for the relegation battle between the league's bottom two teams.
Gordon Thomson, the Grammar president, told Herald Sport: "This matter has caused uproar among our supporters this week.
"Andrew Cramond, our second-row, has been selected to play for the Scotland Under-20s, which we are delighted about. He played in the U20s against the Scotland Clubs side at Netherdale on Wednesday.
"Our winger, Erland Oag, was asked to travel to Netherdale to represent the club international side, without any permission being sought from Aberdeen Grammar. Both played well and scored for their respective sides. We were then informed that as Andy had played a game this week he could not play again on Saturday as they are only allowed one game per week.
"No thought seems to have been given to playing Erland Oag at Netherdale when he has to play at Currie on Saturday. To compound the situation, Edinburgh have released Sean Cox and the Scotland 7s player Andrew Turnbull to Currie.
"Subsequently, the Scotland A side decided that Johnny Gray needs game time, along with two other players this weekend, and released him to play for Currie. We understand that Currie have decided to play Cox and Gray. Yet none of the pro draft players in the Scotland A side have been released to Aberdeen.
"If players representing Scotland can only play one game a week, then none of the Scotland A players should be released."
That version of events was rejected by the SRU, whose head of media, Graham Law, said: "Andy Cramond is not a Scottish Rugby contracted player. He has made a decision that, as he is in the Scotland Under-20 squad who open their international programme against Ireland Under-20 next Friday - and he had played in the Scotland Under-20s match against the Scotland Club XV at Gala on Wednesday and felt sore at the end of that game - that he would not be available for the Currie v Aberdeen Grammar game.
"It has been a long-established protocol, of which all RBS Premiership clubs are aware, that members of age-grade international squads generally do not play for their club the week before an international match. From what we can see, no-one in the current Scotland Under-20 squad has been named in a Scottish Premiership club starting team this weekend.
"Jonny Gray has been out injured since November. It is in the player's interest, and the interest of the Scotland A team that he will captain on Friday, that he gets some game time before he leads Scotland A against England Saxons. Currie chose Jonny Gray in the pro-player draft - the same pro-player draft at which Aberdeen Grammar made their choices last August - and thus Jonny Gray will be involved for Currie this weekend."
Another Aberdeen committee member, Neill Montgomery, said: "All season, we have suffered when playing central belt sides who have EDPs [elite development players from the pro teams] to boost their playing strength while we have none.
"Now in this vital match against Currie [at Malleny Park] we have been denied the use of Andy, while Currie have picked Gray. It leaves a very bitter taste. The playing field is not level but tipped clearly in favour of Currie."