Andor confirmed that the European Commission has a "real concern" about social unrest in certain countries where the "financial panic has been out of control".
He described the need for tough austerity measures in hard-hit countries such as Greece as "inevitable", adding, however, that EU financial support should help to prevent any severe escalation.
Andor said that these risks should not affect other countries "where this panic doesn't apply and social unrest can be constrained".
Specifically, it is essential to maintain a strong social dialogue and fully involve social partners in the development of future plans, he said.
Likewise, he said it was vital to bring forward a convincing strategy for growth and jobs, which is why he believes it is "crucial" that EU leaders give political approval to the Commission's Europe 2020 strategy at a 17 June summit in Brussels.
Sense of urgency 'missing', say social partners
Andor was speaking to EurActiv on the sidelines of a 4 June meeting with EU 'social partners', who were presenting the final input of workers' unions and employer organisations to the 'Europe 2020' strategy for growth and jobs.
Workers and employers joined forces in agreeing that an ambitious growth strategy is the only way to ensure economic recovery.
However, Philippe De Buck, director-general of BusinessEurope, said European employers feel a sense of urgency was missing from the strategy.
In response to the escalating risk of social unrest, he said the EU must continue to reform and "correct" the European social model, as this is the only way to "preserve peace" in the long run.
Changes difficult to swallow
Andor argued that while some changes might be difficult to swallow for European citizens, the European way of life in its current form would have to change, for example through people working later in life.
"We have to appreciate that Europeans are living longer, and of course social security systems have to be adjusted to this demographic fact," he said, though he added that "working longer doesn't necessarily undermine quality of life".
While some structural changes are inevitable, Andor argued that the European social model has proven "quite strong and resilient and has helped people in the face of this crisis". The automatic stabilisers and social security mechanisms are "very much appreciated" by EU citizens, he claimed, praising the EU's anti-crisis efforts.
Discussions on these changes are around the corner, he told EurActiv, starting with the launch of a dialogue on social security.
On 23 June, together with Commissioners Michel Barnier and Olli Rehn, Andor will launch a Green Paper on Pensions, though he cautioned that the latter "is going to be a longer-term discussion, because we don't like to make improvised decisions on issues that will affect the structure of society".