Webb said the government stood to lose tens of millions of pounds in tax revenue every day if the fields were shut and warned it would take time to restart production after the strike ended.
"Restarting cannot happen at the flick of a switch," he said. "It would take several days to re-start safely."
British gas prices surged over 10 percent on Thursday on worries about North Sea supplies.
The National Grid said any closure of the refinery should not cause gas supply shortages as demand is low due to the spring weather and alternative supplies are available.
The strike has led to queues at petrol stations in Scotland as drivers filled up ahead of the weekend.
Business Secretary John Hutton told parliament on Thursday that fuel stocks and imports should be sufficient to maintain supplies during the strike at the refinery.
"Industry has also advised us that, at present, fuel stocks at Grangemouth, together with imports of finished product through Grangemouth to replace lost production should be sufficient to maintain supplies through the period of the industrial action and the consequent restarting of the plant," Hutton told parliament.
Production at the refinery has completely stopped as units shut gradually over the last week, the UNITE trade union said.
The plant's owner Ineos was not available for comment.
Around a quarter of the refinery's output is diesel and worries about the impact of the strike sent London gas oil futures, a benchmark for European diesel and jet prices, rallying to a new record high of $1,080.75 a tonne.
Barges of diesel fuel in Europe's Amsterdam-Rotterdam-Antwerp refining hub traded at premiums of at least $51 per tonne to benchmark London ICE gas oil, an $11 gain from the previous evening.
