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Last week a High Court judge said the curb meant "real misery" for families with children aged under two.
Labour's Debbie Abrahams told the BBC the party would consider removing the £20,000 limit on household benefits if it came to power.
Ministers say the cap encourages work and help is on offer for lone parents.
The cap, first introduced in 2013 but reduced in 2016, limits the income households receive in certain benefits. The idea behind it was that no household should get more in benefits than the average working household.
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The cap now stands at £23,000 for those in London and £20,000 a year outside London. Parents must work for at least 16 hours a week to avoid the cap.
But four lone parent families won a judicial review last week. Their solicitor said their benefits were, or were expected to be, cut as they were unable to work the 16 hours required.
The government says it will appeal against that ruling.
Mrs Abrahams, the shadow work and pensions secretary, said a Labour government would "make sure we would uphold the ruling from the court decision".
Asked whether the cap would go altogether under a future Labour government, Mrs Abrahams said: "We would be looking to see how we do that."
She admitted that Labour had not yet costed the measure but said: "We know that, for example, the court ruling is about £50m so it's not an astronomical figure."
She said she recognised that for some people the capped level "might seem like an awful lot of money".
However, she highlighted "the implications for people in the poorest circumstances, the implications around child poverty which affects children not just while they're young but for the rest their lives - it affects how their brains develop and everything."
Last week a judge in London ruled he was "satisfied that the claims must succeed" against the work and pensions secretary.
Mr Justice Collins said: "Whether or not the defendant accepts my judgment, the evidence shows that the cap is capable of real damage to individuals such as the claimants.
"They are not workshy but find it, because of the care difficulties, impossible to comply with the work requirement."
The solicitor who represented the claimants said she thought around 17,000 families were affected by the cap in this way.
A Department for Work and Pensions spokeswoman said: "The benefit cap incentivises work, even if it's part-time, as anyone eligible for working tax credits or the equivalent under Universal Credit, is exempt.
"Even with the cap, lone parents can still receive benefits up to the equivalent salary of £25,000, or £29,000 in London, and we have made discretionary housing payments available to people who need extra help."