The cross party committee said the number of customs declarations which HM Revenue and Customs must process each year could increase nearly five-fold after Brexit - from 55 million to 255 million.
She said HMRC is under considerable pressure to deliver CDS on time but does not yet have the funding to increase its capacity to cope with Brexit or develop contingency options.
According to the PAC report, HMRC's "main contingency option" - if CDS fails - is the current CHIEF system, which would need a £7.3m cash injection to upgrade it so it could handle 255 million declarations.
These include "scaling up" the CDS service to handle 255 million declarations and ensuring a viable contingency option is in place well before January 2019.
The committee's chairwoman, Labour MP Meg Hillier, said: 'Failure to have a viable customs system in place before the UK's planned exit from the European Union would wreak havoc for United Kingdom business, trade and our worldwide reputation.
"The Treasury needs to ensure there is funding in place to develop contingency options so that there are no barriers to continuity of service", it said.
"Any failure in the new Customs system would most likely lead to huge disruption for businesses, with significant delays at ports and airports of entry".
Despite this, top officials from the tax agency have told MPs the programme is on track and well governed, but have admitted that some risks remain that could jeopardise the already tight timetable.
In 2015, around 55 million custom declarations were made by 141,000 traders.
HMRC started planning to replace CHIEF in 2013-14, well before the EU Referendum following changes to EU legislation which would have been costly and hard to make on CHIEF's ageing technology. HMRC has also said it won't know the cost of upgrading CDS to deal with the increase in declarations until January 2019.
But HMRC does not yet have the funding to increase the capacity of its new Customs Declaration Service to deal with the consequences of Brexit, The House of Commons Public Accounts Committee committee said.
Its report warns that "much remains to be done" to have an effective CDS system in place on time. "This compares to over 6,000 trusted traders in Germany". As part of its plans to broaden engagement with traders, it should also promote the benefits of obtaining trusted trader status and aim to increase the number of registered traders, the PAC said. However, CDS was originally created to handle 150 million declarations each year.