On Wednesday, the U.K. triggered Article 50 of the Treaty of Lisbon, which began the formal two-year process of Britain's departure from the EU.
Burwell told "Closing Bell" she expects companies that are in the U.K. because they want easy access to the EU are going to rethink their location. She thinks they may move all or part of their operations to Germany or Ireland.
Plus, while Britain is talking about international trade deals it wants to negotiate, those will actually take several years to complete because most of their negotiating partners will wait until the final deal between the U.K and the EU, she explained.
"It's a long way away before they have these trade deals that they are kind of pinning their future on," said Burwell.
Naeem Aslam, chief market analyst at TF Global Markets, thinks if there is a "fruitful negotiation" on the Brexit deal, then the pound, equities and investor confidence will rise in Britain.
However, "if this negotiation process derails and we have no deal in the next two years, then certainly the U.K. is not a market that you want to look at," he said on "Closing Bell."
Meanwhile, there is another big risk to the European economy right now — the upcoming presidential election in France, Burwell said.
Far-right presidential candidate Marine Le Pen has vowed to renegotiate the terms of France's membership in the EU and leave the euro.
"A win by her in France … is likely to be more destabilizing for the continental European economy than will be the Brexit negotiations," Burwell predicted.
On Tuesday, UBS said Europe could encounter a shock wave up to five times as turbulent as the start of the euro zone debt crisis if Le Pen is victorious.
— CNBC's Sam Meredith contributed to this report.