Defence Secretary Philip Hammond said the memo, written by a junior army officer, was "incorrect".
Labour leader Ed Miliband said it was the government's duty to "do right by our armed forces".
The document is thought to have been distributed to commanders in Afghanistan.
Some 7,000 army troops will be laid off as part of the first tranche of redundancies, which has already begun.
The Army announced in September it would be telling about 920 people they would be made redundant as part of the cuts.
Earlier reports had suggested the second tranche would add 5,000 to that number by April 2015, but the new memo puts the figure much higher.
But Mr Hammond said: "We haven't changed our position, my predecessor announced the reductions in force numbers that the Army will achieve over the remainder of this decade to 2020.
"We have no plans to change those numbers. Anyone who is injured and who is receiving medical treatment will not be considered in any way for inclusion in a redundancy programme until after their treatment is complete."
A Ministry of Defence statement said the Army was "still considering the criteria including size and shape for Tranche 2 and any subsequent redundancy, and nothing has yet been agreed."
The Chief of the General Staff, Sir Peter Wall, said: "The Army is reducing in size over the next few years and a redundancy programme, although deeply regrettable, is unavoidable.
"Those injured on operations will continue to get the best medical treatment and after-care the Army and the nation can provide. There is no question of wounded soldiers being made redundant whilst their recovery is best served by remaining in the Army."
He said the Telegraph story was a "distortion of the facts".
Soldiers 'outraged'
Commodore Clive Walker, joint force support commander in Afghanistan, said the army was "just scoping all of the options that are open".
But the Telegraph reports that the memo has "been seen by soldiers serving on the front line in Afghanistan, who are outraged".
The mother of Lance Bombardier Ben Parkinson, who lost both legs and suffered brain damage from a roadside bomb in Afghanistan in 2006, said wounded personnel should not be forced out too soon.
"It's very difficult if you are not fit enough to return to your army job but you aren't fit enough to return to a physical career outside of the Army, then what is there for you?" said Diane Dernie.
"And surely in an organisation the size of the MoD, there must be some leeway to employ some of those who are wounded who want to remain in service."
Shadow defence secretary Jim Murphy said the government's "strategic shrinkage" of the armed forces was "being done by stealth".
He said: "No-one should be sacked because they are seriously injured while defending our country.
"This weekend is about remembrance not argument.
"The government should be doing everything in its power to support people in to new roles in the forces, in the MoD or to a new career outside of defence.
Former Royal Navy officer Lewis Page said other cuts should be made before injured soldiers were Former Royal Navy officer Lewis Page said other cuts should be made before injured soldiers were targeted: "The Royal Navy has enormous numbers of senior officers bluntly sitting around not doing anything that possibly justifies their rank and pay."
The leak came as the government pledges to improve access to housing for ex-services personnel.
Housing minister Grant Shapps told Sky News they should be prioritised on social housing waiting lists and government first-time buyer schemes, and there should be increased funding to adapt homes for wounded personnel and to stop so many ending up sleeping rough.
Special ops during the Normandy landings and some very sneaky, hairy stuff in Burma are the two things I know he definitely did. An amazing man to talk to.