The Archbishop of Canterbury has warned that the new visa rules will have an “negative impact” on family relationships.
Justin Welby said the government was “rightly concerned” with cutting migration.
But he said higher income requirements would see many families unable to live together.
From next spring, Britons who want to bring a foreign family member or partner to live with them in the UK must earn at least £38,700 a year.
The government said the increase from the previous limit of £18,600 “reinforces that all those who want to work and live here must be able to support themselves”.
The new figure is above the median gross annual earnings for full-time employees in the UK, which was £34,963 in April 2023.
Overseas care workers will also no longer be able to bring family dependants, such as their partner or children, with them to the UK.
The changes were part of a package of measures announced earlier this week aimed at cutting net migration – the difference between the number of people coming to live in the UK and those leaving – after the figure reached a record 745,000 last year.
Speaking in the House of Lords, the archbishop said: “This week we hear that many people in this country will be prevented from living together with their spouse, child or children … as a result of a big increase in the minimum income requirement for family visas.
“The government is rightly concerned with bringing down the legal migration figures and I’m not, you’ll be relieved to know, going into the politics of that.
“But there is a cost to be paid in terms of the negative impact this will have on married and family relationships for those who live and work and contribute to our life together, particularly in social care.”
He argued the family was “indispensable to the state” and “a lack of strong families undermines our whole society”.
“Government needs families to work. They must not set a series of hurdles for them to jump over,” he added.
The archbishop’s comments came during an annual debate he leads in the House of Lords, with this year’s topic “Love Matters”, The Report Of The Archbishops’ Commission On Families and Households.
Some Conservatives have also raised concerns about the policy.
Former Tory minister Gavin Barwell said: “It is both morally wrong and unconservative to say that only the wealthiest can fall in love, marry someone and then bring them to the UK.”
Tory MP Alicia Kearns told LBC she was “very uncomfortable” with increasing the income requirement for family visas.
“It risks being very unconservative,” she said, adding that the Conservatives were “the party of family”.
Dr Madeleine Sumption, director of the University of Oxford’s Migration Observatory, said the largest impact of the change would fall on those who tend to earn lower wages, including women, younger people and those living outside of London and south-east England.
Labour has said it has “real concerns” about increasing minimum salary requirements for family visas.
On Wednesday a spokesman for Labour leader Sir Keir Starmer said the party wanted to look at the evidence on what impact the change would have, but added: “It looks like it would punish those who fall in love with someone from another country if they don’t earn almost £40,000 a year.”
Earlier this week, No 10 clarified that the minimum income figure was for a “household as a whole”.
The prime minister’s spokesman said people could also demonstrate their ability to support a dependant through their level of savings.
He added that the rules included a provision for “exceptional circumstances where there would be unjustifiably harsh consequences” if an individual earning below the threshold could not bring their foreign family member to the UK.
But the spokesman could not give any examples, saying applications would be considered on a “case-by-case basis”.
There is uncertainty over whether the new income rules will apply to people who already have a foreign family member in the UK, when their existing visa comes up for renewal.
On Thursday, Downing Street said work was “ongoing” to look at how the change would apply to those renewing visas.