FIFA president Gianni Infantino has urged football organisations "not to panic" when it comes to taking measures to prevent the spread of the coronavirus.
Several sporting events have been postponed and the football calendar has also faced problems, with Serie A having called off several fixtures over the past two weekends.
The Swiss government issued a ban on events where more than 1,000 people were expected to be in attendance, with the country's Football Association postponing league matches until March 23.
Some Premier League clubs have banned handshakes at training grounds amid fears matches in England's top flight may be affected.
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Infantino, who last week admitted international matches scheduled to take place this month could be postponed as the outbreak continues to escalate, called for a considered approach to tackle the problem.
"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," he said at the UEFA Congress in Amsterdam.
"It is important to consider all the information from the authorities, but it's also important not to panic. Those who have to take decisions, like happened in Switzerland, will take decisions and then be able to move forward.
"Someone said to me football can be an antidote to coronavirus. I wouldn't go that far, but sometimes football is an antidote to many other illnesses like discrimination and racism, and this is a fight we need to fight all together."
One particularly problematic area for UEFA is the staging of Euro 2020 over 12 countries, with play-offs for the tournament taking place in two weeks.
General secretary Theodore Theodorakis said: "We are taking contact with the World Health Organisation and the different governments. We have to deal with it on a case by case situation. We do not want to overreact but we have created a line of contact.
"We have also had a meeting with the European Leagues [association] to create a coordinating group to find the best possible solutions. The calendar is already congested so working together is where we want to find the solutions.
"There are also different scenarios for the more urgent matches in two weeks' time."
UEFA chief Aleksander Ceferin remained optimistic European football is ready to tackle the issue.
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He said: "We have security concerns, political instability concerns and one of the concerns is the virus. We are dealing with it and we are confident we can deal with it.
"Let's try to be optimistic and not think about dark scenarios. There's time for that later."
President of the Swiss federation Dominique Blanc was particularly foreboding with his warning.
"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 club competitions," he told the 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."