The email sent on Friday by William Shapcott, director-general of the Council for organisational development and services, said the man had attended a meeting of ambassadors of the 27 member states on March 2. All areas where he had been were sealed off and thoroughly cleaned.
The Council, which hosts ministerial meetings and EU summits, has a staff of around 3,000.
All scheduled meetings, including EU trade ministers talks on March 12, will go ahead and "no decision have been taken on a reduced programme", the email said.
A spokesman for the Council was not immediately available to comment on Sunday.
Last week, another EU body, the European Defence Agency, reported a case of coronavirus among its staff. The official had recently travelled to northern Italy.
The European Parliament has moved a plenary session that was scheduled for next week in the French city of Strasbourg to Brussels because of concerns about the coronavirus risk.Separately, Belgium's health ministry said on Sunday the number of coronavirus cases in the country had reached 200. It said the virus had started to circulate locally among the Belgian population.