The WHO said the virus behind the Covid-19 pandemic was still circulating and countries need to sharpen up their response systems.
Several high profile athletes have suffered from Covid-19 at the Paris Games.
British swimmer Adam Peaty tested positive a day after winning silver in the 100m breaststroke when he had not felt well, his team said. Australian medal hope Lani Pallister pulled out of the women's 1500m freestyle after falling ill.
Data from 84 countries shows that the percentage of positive tests for SARS-CoV-2 -- the virus that causes Covid-19 disease -- "has been rising for several weeks", said Maria Van Kerkhove, the WHO's epidemic and pandemic preparedness and prevention director.
Furthermore, wastewater surveillance -- which tends to give a two-to-three-week advance indication on case numbers -- suggests that circulation of SARS-CoV-2 is "two to 20 times higher than what is currently being reported", she told a media briefing.
"This is significant because the virus continues to evolve and change, which puts us all at risk of a potentially more severe virus that could evade our detection and/or our medical interventions, including vaccination."
Van Kerkhove said the high circulation was not typical for respiratory viruses that tend to increase in circulation in the colder months.
However, "in recent months, regardless of season, many countries have experienced surges of Covid-19, including at the Olympics, currently, where at least 40 athletes have tested positive," she said.
"It's not surprising to see athletes being infected, because as I said before, the virus is circulating quite rampantly in other countries."
