From next April, employers will have to pay NI at 15% on salaries above £5,000, instead of 13.8% on salaries above £9,100 currently.
The change is set to raise £20bn a year, making it one of the biggest single tax-raising measures in history.
Sainsbury’s chief executive Simon Roberts said on Thursday the NI changes would cost the business around £140m, a sum which does not include the increases to minimum wage.
“I don’t think you can shy away from the fact that, because of the changes in everyone’s cost base, it is going to feed through into higher inflation,” he said.
“We will do everything we can to mitigate the impact, like you’ve seen over the last four years, to really improve our pricing position.
“But this barrage of costs coming at us is significant and we’re an industry, a very efficient industry and intensely competitive, and there just isn’t capacity to absorb all of this.”
His comments come after Marks & Spencer chief executive Stuart Machin said on Wednesday the supermarket could not rule out price rises following the Budget.
Mr Machin said he “didn’t quite see the double whammy coming up”, referring to both the NI rise for employers and the reduction of the threshold for it applying.
Asked directly if this would mean higher prices, he said: “I can’t rule out anything because it’s still early days in our planning.”
He estimated that the NI change and the increases to minimum wage would cost the business £120m.