The German Head Coach made 10 changes to the starting 11 which secured the club's SkyBet Championship Play-Off place with victory at Wolverhampton the previous Tuesday evening.
Town went on to lose the game 2-0 to relegation threatened Birmingham who also had Che Adams sent-off in the 23rd minute.
The home win was Harry Redknapp's first in charge of the club and only the third in 24 Championship games, lifting the Blues to 20th in the table and two points clear of the bottom three.
And with Blackburn Rovers and Nottingham Forest just below the Blues heading into the final day of the season, Wagner has come in for criticism from many for what was perceived as a weakened side when the stakes were so high for other clubs.
Speaking earlier to Sky Sports, an EFL Spokesman said: "EFL rules state all clubs are subject to the requirement to play their strongest side in all SkyBet League matches unless some satisfactory reason is given.”
The EFL statement, published on their official website, said that if they did not find Huddersfield Town's response to the changes satisfactory, then it will take the matter further.
However, the statement added “that the result of Saturday’s game will stand in all circumstances and any potential action would be taken against Huddersfield Town directly.”
Although there is no threat of a points deduction, the club could be set for hefty fine should the Football League think the changes were unacceptable in accordance to the rules of the game.