The Force India driver had secured fifth on the grid on home soil, but now looks set to lose it after the stewards found his car to be below the minimum 642kg weight.
A report by the stewards revealed that di Resta's car weighed 641.5kg at scrutineering, which is 0.5kg below the minimum weight required for the car.
The car was reweighed without fuel on board and weighed just 640kg, 2kg below the minimum weight limit.
A calibration check of the scales used by the FIA showed they weighed 599.5kg when checked with 600kg of weight, which is still 1.5kg below the minimum weight limit.
The matter has been referred to the stewards, who are likely to exclude the car from qualifying for the infringement unless there are exceptional circumstances.
A likely penalty would be relegation to the back of the grid.
Speaking earlier about his performance, di Resta had admitted that he was 'shocked' at the performance.
"The car is obviously working well," said di Resta. "Yesterday we were P4 and I was surprised we were there. So I'm a bit shocked we are still only one position behind that today.
"But ultimately it's in our window. We went a bit backwards with set up before FP3, but the guys put in a tremendous effort to get the car ready for qualifying."