Mr Barroso said Brexit will open up a path for Mr Juncker to promote his vision for a more federal EU.
Speaking to the BBC, the former Portuguese PM said: “Now that Britain is leaving the proportion of the economies in the European Union that are in euro will be much higher.
“I think we have to make our plans for the European Union such to avoid artificial divisions. Flexibility yes, but not stratification.
“We cannot have first and second class members in the European Union.”
President Juncker presented plans to bring more EU countries under a common monetary and military policy during his State of the Union speech in early September.
His proposals garnered the support of French President Emmanuel Macron who, alongside Germany, holds the key for the development of the EU.
Mr Barroso added: “France and Germany are indispensable. Without them nothing can happen in the European Union.
“I welcome all the efforts for a stronger relationship and cooperation between those two countries. Having said that, any hierarchy of countries in the European Union is not good.”
It is believed Brexit will allow pro-European leaders to pursue a reform agenda leading to the federalisation of the EU.
Charles Grant, head of the Centre of European Reform, said the EU viewed the UK as an obstacle “blocking” all attempts of change within the institution.
He said: “The British have have obviously been a problem in the past, blocking integration in certain ways, opting out of things and Juncker says ‘well, the British are out of the way. Why don’t we just get everybody to move forward together.’”
Mr Grant said EU Commissioner Juncker had embraced a return to the past, presenting a plan for the future of the European Union reminescent of “old-fashion European thinking.”
He continued: “To me, the Juncker speech is a revival of old-fashioned conservative, federalist European thinking.
“He said he wanted everybody in the euro, everybody in the Schengen area of free travel, everybody in the banking union!”