Revenue has said the number of applications for a key customs registration number so far this year has already almost reached the total for all of last year.
Having an Economic Operators Registration and Identification (EORI) number is the minimum requirement for businesses to be able to move goods to, from or through the UK from March 29.
Revenue said 2,617 such registrations have been made so far this year, compared with a total of 2,976 for all of 2018.
It noted that in the last seven days, 416 businesses have applied for an EORI registration, while the overall number of Irish businesses with such a registration stands at 42,662.
Lynda Slattery, Head of Revenue's Brexit Policy Unit, said if a business does not have an EORI, it is running a "real and unnecessary risk" of experiencing significant delays and problems moving their goods after Brexit.
Ms Slattery urged businesses to act immediately.
"Applying for your customs (EORI) registration is free and can be completed quickly and easily through Revenue's secure online services," she said.
"The figures show that many businesses are already making their preparations. If you currently trade with or through the UK, or even if you are thinking of trading with the UK post Brexit, make sure you get your customs (EORI) registration number now," the Revenue official urged.
Revenue also reminded businesses that in order to move or continue to move goods to from or via the UK post Brexit, there are a few basic steps that every business should take now to be ready.
As well as applying for their customs (EORI) registration, businesses should ensure they have the facility to make a customs declaration while they should also know the Commodity Code of the goods or products they will import or export.
"These three elements are at the heart of a business being able to move goods through, to and from the UK post Brexit," Revenue stated.