The chair of the Treasury select committee has written to HMRC seeking clarification on what proposed new VAT rules will mean for companies.
Legislation that plans to change how imports from EU countries will be treated after Brexit has been drafted.
The Customs Bill will have its second reading in the House of Commons on Monday.
It could force tens of thousands of firms to pay VAT upfront in cash to HMRC.
Nicky Morgan, chair of the Treasury committee, said she would contact HMRC and will propose that MPs investigate the matter.
As Brexit comes closer, "we are beginning to see the reality of how it will bite", she said.
Under existing rules, goods imported from the EU are referred to as "acquisitions" for tax purposes.
No VAT is paid until the products have been sold to the final customer and paid for.
But unless the UK remains in the Customs Union, goods from the EU will have to be treated like all other imports after Brexit and will attract VAT by the 15th day of the following month.
The British Retail Consortium said it was concerned about the government's lack of strategy about VAT.
Helen Dickinson, its chief executive, said: "It's ridiculous to assume that it would be easy to bring forward the timings on such significant amounts of cash.
"To plan ahead, retailers need to know what their liability on tax will be, and what measures are going to be taken to avoid this hit to cash flow with new costs on importing goods from Europe and higher potential pressure on prices for ordinary shoppers."
She added: "Resolving this uncertainty can be achieved by securing a deal between the UK and EU on VAT and through policy measures adopted by HMRC like self-assessment."
The Treasury acknowledged in the Budget in November that businesses benefit from postponed accounting for VAT when importing goods from the EU.
"The government recognises the importance of such arrangements to business, due to the cash-flow advantage they provide.
"The government will take this into account when considering potential changes following EU exit and will look at options to mitigate any cash-flow impacts for businesses," the Budget statement said.
The Budget also stated that ministers aimed to keep tax arrangements "as close as possible to what they are now" after Brexit.