"We should be prepared that it will remain with us," the head of the Stockholm-based European Centre for Disease Prevention and Control said in an interview.
"It seems more likely that it would stay. It seems very well adapted to humans," she said.
"It wouldn't be the first virus that is with us forever, so it's not an unusual feature for a virus."
While vaccines dramatically reduce the risk of contracting the illness caused by Covid-19, scientists have not yet established with certainty whether vaccines also reduce transmission of the virus.
There is also particular concern that the vaccines may not be as effective against some variants of Covid-19, especially the South African and Brazilian ones.
"The question is what it then means in terms of the changes of the virus for the vaccine effectiveness," Ammon said, citing the seasonal flu as an example where vaccines are adapted annually.
"It might turn out that (the coronavirus) goes the same way, or that at one point it remains stable and we can use one vaccine for a longer period," she told AFP.