Eluned Morgan said police in the Dutch city had said they will not be “letting Welsh fans into the country”.
The Netherlands is on the UK’s amber list, meaning travel is not advised, while the UK is not on the list of safe countries compiled by the Netherlands which hosts the last 16 game on Saturday.
Small numbers of Welsh supporters were allowed at their earlier games in Baku, Azerbaijan, and in Rome where they played Italy.
Speaking at Monday’s Welsh government coronavirus briefing, Baroness Morgan said: "We have had some guidance from the police in Amsterdam who have told us that they will not be letting Welsh fans into the country.
"And so that means that we would encourage you of course to stay here and watch the matches carefully.
"If local authorities come forward and ask us for the setting up of fan zones, then of course we will as a government consider that and publish guidelines for how that could be done in a safe way."
She said she had watched the scenes of massed ranks of Scottish fans in London “with horror” and added that the the government was "far more keen" to see people watching the match outdoors if possible “in a controlled setting”.
Wales, semi-finalists at the last European Championship five years ago, qualified for the last-16 by finishing above Switzerland, ranked 13th in the world, and a much-lauded Turkey team.
They will play Denmark after the Danes beat Russia 4-1 at home in Copenhagen and Belgium beat Finland.
It will be an emotional night for the Danish team whose first game was marred by the collapse on the pitch of star player Christian Eriksen who suffered a heart attack.