As of 2012, Britons must earn more than Â£18,600 before a husband or wife from outside the European Economic Area (EEA) can settle in the UK.
Critics claim 15,000 children have been separated from parents because of it.
The rule was introduced by the former coalition government to stop foreign spouses becoming reliant on taxpayers.
If the government loses, thousands of couples who currently live outside the UK could move to Britain.
The minimum income threshold, which also affects people settled in the UK as refugees, rises to Â£22,400 if they have a child who does not have British citizenship - and then by an additional Â£2,400 for each subsequent child.
These thresholds replaced a previous, more general requirement to show the Home Office that the incoming partner would not be a drain on public resources and that the couple or family could adequately support themselves.
The current rules do not take into account the earnings of the overseas partner - even if they have higher qualifications, or are likely to be employed in higher-paid work than their British spouse.
The minimum income threshold does not apply to spouses from within the EEA.
In a series of test cases, affected couples argued that the rules breached their right to family life.
Two of the claimants, Abdul Majid and Shabana Javed, are British citizens who have partners who are Pakistani nationals.
The third claimant is a Lebanese refugee who cannot find suitable work in the UK despite his postgraduate qualifications. He says his similarly-qualified wife has high earning potential and speaks fluent English.
The final case concerns another recognised refugee from the Democratic Republic of Congo whose wife has been barred from settling.
In 2013, the High Court ruled in the couples' favour saying that the rules were "onerous and unjustified" - and the judge urged the home secretary to rewrite them.
That decision was overturned at the Court of Appeal, leading to the challenge reaching the Supreme Court.
If the Supreme Court rules against the government, it could lead to the minimum income threshold being lowered or, potentially, require Parliament to reconsider the entire law.
When the government introduced the measures, it said they aimed to reduce the burden on taxpayers, promote integration and prevent and tackle abuse of the family migration route.
But campaigners say that all they have done is split up couples and families for whom the minimum income threshold is unobtainable.
They say that nearly half of the British population earns less than the income barrier, meaning they would be affected if they chose a foreign-born spouse.
The Supreme Court is to rule on whether an income barrier stopping thousands of British citizens from bringing a foreign spouse to the UK is lawful.