The 26-year-old will not play in the T20 World Cup or Ashes later this year.
The 26-year-old has suffered a fresh stress fracture to his right elbow, ruling him out of the trip Down Under as well as the Twenty20 World Cup.
Archer was seen as vital to England’s chances of winning the urn back after his searing pace caused Australia problems in the 2019 series.
Cook fears there may be a lasting effect on Archer’s pace.
Cook said on BBC Test Match Special: “Huge news and very worrying for him. We spoke all this time about England going to Australia with a battery of fast bowlers and Jofra Archer is another one joining Ollie Stone who is out.
“Tim Bresnan was never the same bowler after his elbow injury – they’re so hard to get right. He lost that yard of pace and Jofra’s point of difference is that he can bowl genuinely quick. It’s a game-changer.
“The only thing now, though, is the advances in medical research and recovery of these injuries is better now. So if there is ever a chance, they can get it right.”
The bad news keeps on coming for England, who are up against it in the first Test against India, following news that Ben Stokes is taking an extended break from the game.
Former captain Michael Atherton said on Sky Sports: “Bad news for him, terrible news for England, that bad news keeps coming in waves, on the back of Ben Stokes, so you have a couple of pillars of your first choice team there when you are thinking about this series and the Ashes this winter.
“For a while Chris Silverwood has been hoping and trying to get a squad of fast bowlers together.
“The history of the game tells you that fast bowlers win Ashes series in Australia.
“England don’t win many series Down Under, generally good quality fast bowlers win Ashes series and what Silverwood was hoping was to get a group of them together, of which Archer would be the spearhead.”
Atherton accepts there could be doubts over Archer’s Test career given his injury problems.
“Possibly, we shall wait and see. Fingers crossed that is not the case,” he said.
“He has gone on record as saying he wants to play Test cricket and play all formats.
“All the top players still want to prove themselves across all formats. Let’s hope his body allows him to do that and that he is not just reduced to playing short-form cricket.”