Following the controversy, Ms Murty declared that she would pay UK taxes on all her worldwide income.
During the furore, Sajid Javid, the Health Secretary, also announced that he had held non-dom status for six years while working as an international banker before entering politics.
Ms Reeves said on Monday: “As the Tories raise taxes on working people, it simply isn’t right that those at the top can benefit from outdated non-dom tax perks.
“With Labour, people who make the UK their home will contribute to this country by paying tax on their global income.”
The opposition party said its policy, which is part of a wider review of the current tax system by Ms Reeves, would end the 200-year-old rules that mean domicile is passed down through someone’s father.
Party aides said the reforms would bring Britain into line with other major economies such as France, Germany and Canada.
According to a party briefing paper, 1,900 non-doms who have been in the UK for between seven to 15 years currently pay a charge to keep their tax avoidance status.
Charges range from £30,000 to £50,000 per annum, raising around £70 million per annum.
Labour said that total indicated non-doms are securing “significantly more” than £70 million in tax reductions, citing a study by the EU Tax Observatory which estimated the fiscal gain of eliminating non-dom rules could be more than £1 billion.