The injury happened during England's record 36-0 World Cup defeat against South Africa at Stade de France on Friday night.
England have not decided on his World Cup replacement yet, but Noon's Newcastle colleague Toby Flood is favourite to take over.
While England team doctor Simon Kemp was able to deliver positive medical bulletins on Jason Robinson (hamstring), Jonny Wilkinson (ankle ligament sprain) and Olly Barkley (hip), 27 times-capped Noon's World Cup is over.
He said: "I am getting used to the slow realisation that my dream of playing in the Rugby World Cup is over, but what is hardest is that I have only been here for two weeks and played just two games.
"However, I also know that I will be home soon and I will be there for my daughter's first birthday, so I have been thinking about that as well.
"I was running down the blindside on the right hand side of the pitch with a few minutes to go in the second half.
"I bounced off a couple of bodies and I had the ball when another player landed on my leg. I felt my knee pop, so I knew it had gone.
"The scan I had just confirmed how long I would be out for.
"I received a lot of help from the England medical team, and I will be looked after by Marten Brewer at Newcastle Falcons when I get home.
"Initially, I was obviously gutted to be out, and I have asked myself a few 'what if' questions that led up to the injury, but there is nothing I can do about it now."
A six-week absence is rated the norm for an injury such as Noon's.
England could though, reflect on more encouraging news surrounding Robinson, who pulled up in agony before limping off to a standing ovation at Stade de France.
And Kemp confirmed that fly-halves Wilkinson and Barkley should be available for selection to face Samoa in next Saturday's critical Pool A clash.
Kemp said: "Jason has sustained a strain to his left hamstring.
"Although he pulled up pretty dramatically during the game, the location and size of the strain leads us to believe he has every chance of being able to pay a further part in the tournament.
"He will stay with us, and we will continue to rehabilitate him.
"We know the recovery from hamstring injuries is often unpredictable.
"There are players who have had fairly low grade hamstring injuries who have struggled for a number of weeks, to other players with fairly significant injuries who have flown through and accelerated the hamstring protocol.
"Jason has never injured his hamstring before, and when he felt his pain, he went to ground almost immediately, therefore preventing any further damage.
"It was pain that brought him down, rather than a loss of power.
"The location of the strain is between two of the hamstring muscles, rather than within the muscle itself. We are confident he may make a much swifter recovery than might have been anticipated.
"He is having ice, gentle massage and a number of electro-therapies with the aim being to try to disperse the swelling and the little bit of bleeding that has accumulated."
Wilkinson and Barkley suffered their injuries during training, but with Ashton set to announce his starting line-up against Samoa, both players could feature.
Kemp added: "Jonny and Olly have continued to make very good progress from their injuries, and we've always anticipated they would be available for selection for next weekend.
"Nothing has happened over the past few days to change that view, and I think that will become clearer when Brian announces his side.
"Jonny's ankle got caught in a ruck that developed around a tackle, and you have to make a choice as to whether you have your players involved in contact in training or not.
"We believe we go to every length to ensure they take part in contact where appropriate to enable the team to prepare, but not unnecessary contact."