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While speaking to journalists she said the Houses of Parliament could see a fire like the one that damaged the Notre-Dame cathedral in Paris.
Parliament needs urgent repair work that could cost between £7bn and £13bn.
A recent report said costs could be kept down if MPs and peers left while the building work was carried out.
However, some politicians have expressed concern about moving out amid plans to relocate to Richmond House in central London were vetoed.
In 2019 a major fire engulfed Notre Dame, destroying the 850-year-old building's Gothic spire and roof.
Speaking to Radio 4's Week in Westminster programme, Ms Leadsom said the same thing could happen in Parliament, adding that a fire in 2017 was only averted because of the presence of the 24/7 fire patrol.
"That is so 'there but for the grace of God'," she said.
"It could burn down today, tomorrow, any day and we've got to make that decision and get on with it."
The Houses of Parliament - which was built between 1837 and 1860 - requires significant restoration, including asbestos removal, fire safety improvements, renewal of wiring and conservation work.
In addition to a fire risk, there have been warnings the building could be damaged by a flood of sewage. A sewage ejector system installed in 1888 is still in use now.
In 2019, MPs voted to set up a sponsor body with responsibility for the restoration of the building.
A review produced by the body put the basic costs of essential repairs at £7bn-£13bn and estimated they would take between 19 and 28 years to complete - or 12 to 20 years if the building was fully vacated.
It said the costs would increase by 40% if politicians stayed put.
Expressing concern about the project's timescales and costs, the commissions - or administrative bodies - for the House of Commons and Lords voted to scrap the sponsor body in favour of a "new approach".
The commissions also agreed to seek approval from MPs for a "revised mandate" for the project.
09 April 2021
04 March 2021
24 October 2019