Without the drugs used to fight infections, common medical interventions such as caesarean sections, cancer treatments and hip replacements would become incredibly “risky”, she said.
And transplant medicine would be a “thing of the past”, she added.
“We really are facing, if we don’t take action now, a dreadful post-antibiotic apocalypse,” she told the Press Association.
“I don’t want to say to my children that I didn’t do my best to protect them and their children.”
Health experts have previously warned that resistance to antimicrobial drugs could cause a bigger threat to mankind than cancer.
In recent years, the UK has led a drive to raise global awareness of the threat posed to modern medicine by antimicrobial resistance (AMR).
Around 700,000 people around the world die annually due to drug-resistant infections including tuberculosis (TB), HIV and malaria.
If no action is taken, it has been estimated that drug-resistant infections will kill 10 million people a year by 2050.
Dame Sally said that because AMR is “hidden”, people “just let it pass”.
The comments come as the UK Government and the Wellcome Trust, along with others, have organised a “call to action” meeting for health officials from around the globe.
At the meeting in Berlin, the Government will also announce a new project which will map the spread of death and disease caused by drug-resistant “superbugs”.
Dame Sally told the Press Association: “This AMR is with us now, killing people.
“This is a serious issue that is with us now, causing deaths.
“If it was anything else people would be up in arms about it. But because it is hidden they just let it pass.
“It does not really have a ‘face’ because most people who die of drug resistant infections, their families just think they died of an uncontrolled infection.
“It will only get worse unless we take strong action everywhere across the globe.
“We need some real work on the ground to make a difference or we risk the end of modern medicine.”
She added: “Not to be able to effectively treat infections means that caesarean sections, hip replacements, modern surgery, is risky.
“Modern cancer treatment is risky and transplant medicine becomes a thing of the past.”
Dame Sally warned that if the global community did not act then the progress which had been made in Britain may be “undermined”.
She added: “We use more than I would like and we estimate that about one in three or one in four prescriptions in primary care are probably not needed.
“But other countries use vastly more antibiotics in the community and they need to start doing as we are, which is reducing usage.
“Our latest data shows that we have reduced human consumption by 4.3 per cent in 2014/15 from the year before.”
In September the World Health Organisation warned that antibiotics are “running out” as a report found a “serious lack” of new drugs in the development pipeline.
The new project which will map the spread of superbugs is a collaboration between the UK Government, Wellcome Trust, Bill and Melinda Gates Foundation, the University of Oxford and Institute for Health Metrics and Evaluation.
Foreign and international development minister Alistair Burt said the project will help to “pinpoint problem areas”.
He said: “The UK is not content to sit back and let this turn into a catastrophe.
“Part of the problem has been a lack of co-ordination of global efforts and an understanding of where we need to target our future efforts.
“The partnership we are announcing today – part of more than £160m in new research funding in the past year – will help us to pinpoint problem areas.
“This is just one part of our more than £615m investment by the UK Government into tackling drug-resistant infections since we launched our National Strategy at the end of 2013.”
As well as the global project, the Government has also pledged to highlight the threat at home with a domestic awareness campaign which will alert the public to the issue of AMR, reduce their expectation for antibiotics and supporting change among healthcare professionals.
Tim Jinks, head of drug resistant infections at the health research charity the Wellcome Trust, which is investing £2.4m in the mapping project, said: “While we have seen progress in recognition around the world of the threat that superbugs pose, we need to retain momentum. High-level commitments must quickly become action.
“The Global Burden of Disease AMR project will provide vital information on the spread and impact of drug resistance and is one of a number of activities Wellcome is supporting to help address this urgent global problem.
“Together, we can stop superbugs undermining the whole of modern medicine.”
Meanwhile, the Wellcome Trust, along with the UN Foundation, has conducted analysis on global action plans to tackle superbugs.
The research found that while 151 of 195 countries are developing a plan, just one in five commit to reducing antibiotic use, improving hygiene and preserving antibiotics of last resort.
And only 5% are adequately funded and monitored, Wellcome said.
Meanwhile another joint research project has been announced by the Academy of Medical Sciences.
The Academy had pledged to build stronger research links between the UK and India – where it is estimated that 60,000 babies die each year due to drug-resistant infections.
The programme, supported by The Yusuf and Farida Hamied Foundation, will include a visiting professor scheme and two major scientific meetings.
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