Thomas Piketty delivered the stark warning via BBC Newsnight on Friday night. Britain formally left the EU on January 31 and there is speculation over whether other countries could follow.
After the UK’s departure the EU has 27 remaining member states.
Mr Piketty, a French academic, shot to fame following the publication of his best selling book ‘Capital in the Twenty-First Century’ in 2013.
Speaking to BBC presenter Mark Urban he said there is a danger of the EU being hit by “Brexit after Brexit”.
The economist added: “I think there’s a risk.
“You have this popular discontent about the European Union, its not going to go away so you have to do something.
“The question is do you want to control the movement of people, restrict the circulation of labour which has been the Brexit way, or do you want to better control the movement of capital and how much investors are able to avoid taxation.”
Britain voted to leave the EU in June 2016 by a margin of 52 percent to 48 percent.
Implementing the result was repeatedly delayed until January 31, after the Tories won a general election in December.
“The question is who is going to be the next to leave.
“Who is going to be the first to join us and the other 170 odd countries outside the EU, trading with our neighbours but governing ourselves.”
He noted: “There are two ways in which it could happen.
“It could happen accidentally because of some economic shock.
“In that case, I think Italy would a candidate.
“Or it could happen Brexit-style.
“In other words a referendum. Demand for a referendum and a successful referendum.”
“I think I would probably at the moment put my money on the Netherlands.
“But I have to nod in the direction of Denmark, which is also having a similar debate.”
No other country is currently planning a referendum on its EU membership.