Scotland lock Skinner was sent off for a dangerous tackle during last weekend’s 20-19 regular-season victory over Sale, while flanker Ewers was cited for a dangerous tackle in the same game.
The Rugby Football Union said both players appeared before an online independent disciplinary panel and they each received a four-week ban.
It means they will also miss the Premiership final at Twickenham on June 26 if Exeter beat Sale.
The RFU said that both players contested the charges, but they were upheld by the disciplinary panel.
In a statement, the panel said: “Both cases involved direct contact with an opponent’s head that carried a high degree of danger.
“None of the mitigating factors set out in the World Rugby Head Contact Process which would have justified the red card otherwise being reduced to a yellow card were present.
“Neither player accepted the charge and so full mitigation credit was not available to them.”
It is a major double setback for Exeter, who are bidding to reach a sixth successive Premiership final.
Victory over Sale at Sandy Park would book a Twickenham appointment with Bristol or Harlequins.
Asked for his reaction at his weekly media conference, Exeter rugby director Rob Baxter said: “I am very disappointed. If I am honest, I am struggling with the whole process and everything about it a little bit.
“There is a huge amount of inconsistency, a lack of empathy for the players involved in the incidents.
“I definitely think it is getting to the stage that it is something that the players who are currently playing the game need to have, or need to decide through the RPA (Rugby Players’ Association) on how they are going to do it, have a lot more input on how the whole process around making the laws, how they are refereed, cited etc.
“If you ask a lot of the players who are playing now, I don’t think they would agree with what is currently happening.”
Baxter continued: “Everyone has got a responsibility to tackle lower and safely – it is written in stone, we are all aware of it – but rugby is an incredibly dynamic game with a lot of moving parts.
“Sometimes it just feels like where is the empathy, or the understanding of, that mechanism of moving parts, understanding how players move around the field? What is the genuine expectation of what is happening in a game of rugby?”
Sale, meanwhile, will also be without key players for the game, with fly-half AJ MacGinty and flanker Cameron Neild both sidelined because of injuries.