Populist parties have gained appeal with voters in Europe ever since the global financial crisis of 2007-08. Right-wing populist parties outside of Austria include the United Kingdom Independence Party (UKIP), the Front National in France, Alternative for Deutschland in Germany and Golden Dawn in Greece.
"The risk is that Europe continues to produce political risk and political risks are a main reason why investors abroad, particularly outside Europe, don't invest in Europe — so the uncertainty is that the politics this is producing is a real negative for Europe as an investment location and I think that's really the concern I have," Weber told CNBC.
According to ING, the contentious elections in Austria are a clear warning to the rest of the euro zone that, "increasing populism is likely to reduce options for potential government coalitions, limiting common ground for economic policy options, thereby possibly hampering growth and consequently again preparing the grounds for more populism."
Polls suggest Marine Le Pen of France's National Front party is set to progress to the final round of the 2017 presidential election, Wishart noted.
"The performance of the far-right party suggests that a Le Pen presidency in France is not implausible," he concluded.
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—Katy Barnato contributed to this report.