Labour also criticised the plan, with Shadow Home Secretary Diane Abbott saying it will need so many exemptions that the changes are “meaningless”.
The new rules seek to lower the salary threshold for skilled migrants from £30,000 to £25,600 for those coming to the UK with a job offer.
However, the Government said that if the applicant earns less than the required minimum salary threshold - but no less than £20,480 - they may still be able to enter if they have a job offer in a specific shortage occupation or if they have a PhD relevant to the job. There will not be a visa option for low-skilled migrant workers.
Ms Abbott said: "This isn't an 'Australian points-based system', which is a meaningless Government soundbite. It's a salary threshold system, which will need to have so many exemptions, for the NHS, for social care and many parts of the private sector, that it will be meaningless.
"Ultimately, it will also be very difficult to attract the workers we need at all skill levels while the Tories' hostile environment is in place. It needs to go."
Liberal Democrat home affairs spokeswoman Christine Jardine said the proposals were based on "xenophobia" and not the "social and economic needs of our country".
"Too many businesses are already struggling to hire the workers they need, and now the Tories want to stop them recruiting all but the highest paid employees from abroad," she said.
Pro-EU campaign group Best for Britain was also critical of the plans.
Chief executive Naomi Smith said: "Companies are being urged to eliminate low-paid jobs through automation and technology, but the truth is that a great many low-paid workers cannot be replaced by machines, not least in the care sector.
"Couple that with the additional red tape companies will face in ensuring staff can work in the UK, and it becomes clear that this represents a double-whammy to hard-pressed employers who rely on freedom of movement to deliver essential services.
"While concerns over immigration are well documented, we should all be concerned by a policy that actively promotes the elimination of jobs, even low-paid jobs, in pursuit of a short-sighted migration policy."
Dame Donna Kinnair, chief executive and general secretary of the Royal College of Nursing, said: "We are concerned that these proposals from the Government will not meet the health and care needs of the population.
"They close the door to lower-paid healthcare support workers and care assistants from overseas, who currently fill significant numbers of posts in the health and care workforce."
The UK Homecare Association said: "We are dismayed by the decision Government has made.
"Cutting off the supply of prospective careworkers under a new migration system, will pave the way for more people waiting unnecessarily in hospital or going without care.
"Telling employers to adjust, in a grossly underfunded care system, is simply irresponsible."
Unison assistant general secretary Christina McAnea said the plans "spell absolute disaster for the care sector".
The Food and Drink Federation (FDF) welcomed the reduction of the skilled worker salary threshold, but was cautious about the potential impact of the policy on its members due to the sheer number of workers involved in food production.
Mark Harrison, policy manager covering employment and access to labour at FDF, said: "The food and drink industry is reliant on workers at all skill levels.
"We have concerns about access to those potential employees who won't qualify through these 'skilled' routes such as bakery assistants, meat processors, and workers essential to the production of huge array of basic foodstuffs such as cheese, pasta, and sausages."
Carolyn Fairbairn, director general of the Confederation of British Industry (CBI), said: "Getting a new immigration system right on day one will be critical for economic growth and the UK's global reputation as it forges a new path outside the EU.
"Several aspects of the new system will be welcomed by business.
"Nonetheless, in some sectors firms will be left wondering how they will recruit the people needed to run their businesses.
"A regularly reviewed shortage occupations list, with promises of further flexibility, will be vital for the effectiveness of the new system.
"Above all, the Government must work with employers and employees - especially smaller firms - to ensure they have the time to adapt to new policies and practices."
Alp Mehmet, chairman of Migration Watch UK which campaigns to reduce immigration, said the proposals "suggest the government is not serious about taking control of immigration."