In Italy and Switzerland among other European nations, football has ground to a halt due to the spread of COVID-19.
Serie A's Derby d'Italia between Juventus and Inter Milan was called off due to the outbreak in many parts of Italy.
As Europe's continental tournament is only three months away, Infantino addressed UEFA to clarify a way forward amid the chaos of the outbreak.
"Some of you have had to take important decisions in this respect. Every competition organiser has to study it of course and has to take decisions," Infantino said.
Dominique Blanc, president of the Swiss Football Federation, shared concern in response to the structure of the continental showpiece.
"We are facing a situation which could shake professional football to its foundations. So, unfortunately, we will not be able to avoid scheduling postponed matches at the same time as UEFA competitions," he told the UEFA congress.
"If the situation persists we will not be able to avoid talking to UEFA about financial aid. It's a worst-case scenario but it cannot be dismissed out of hand."