Speaking from the audience, the woman highlighted the apparent juxtaposition of Osborne's pledge to reduce corporation tax with the plight of a cash-strapped NHS.
She said: "It's sort of like saying you appreciate Google more than you appreciate the NHS."
Beginning her comments to the panel, the woman said: "You said you'd ring-fenced the healthcare, but it doesn't need ring-fencing, it needs more money."
She continued: "By cutting disability benefit, by cutting social services, all that is doing is bringing the NHS down to its knees.
"The NHS won't be around for another couple of years if you continue to do this."
Osborne was accused of slashing welfare to fund tax breaks for the rich after it emerged that nearly a third of all his Budget cuts will come from disability benefits.
Corporation tax is expected to be reduced from its current rate of 20 per cent to 17 per cent from April 2020, saving UK businesses almost £15billion a year by 2020.
The disability cuts, first unveiled by Work and Pensions Secretary Iain Duncan Smith, will axe £590m in 2017/18 – the same year that the wealthy will gain £630m in capital gains tax relief.
Osborne had described a recent agreement between Google and HMRC as a "major success", despite intense criticism at the size of the internet firm's final tax bill.
Osborne did not use his latest Budget to pledge additional cash for the NHS.
A previous announcement pledged a further £3.8bn for the NHS this year.
At the time, health service bosses said a significant budget increase was needed to stave off problems serving increased demand.
Thursday's Question Time came from Chelmsford, Essex.
Alongside Ukip's leader in the European Parliament Roger Helmer MEP and director of the Institute of Economic Affairs, Mark Littlewood.