She says she hopes the match will be "very fair."
Germany, Europe's biggest economy, has been a major contributor to international bailouts for Greece and was instrumental in demanding structural reforms and hugely unpopular spending cuts in return. Merkel is not a popular figure for Greeks, to say the least.
Merkel can go to Friday's match in Gdansk, Poland, because the Italian government moved up a meeting in Rome with the Italian, French and Spanish leaders that originally was supposed to end as the match started.
The presence of Merkel could add extra political spice to Friday's encounter — though team officials on both sides have been at pains to stress that it is purely a sporting event.
It wasn't clear whether Merkel will meet any Greek officials at the match. New Greece Prime Minister Antonis Samaras was sworn in only Wednesday, three days after Greek elections.
Merkel said she had congratulated Samaras "and I would be glad if he came to Gdansk too; whether he can arrange that, he will have to say himself — I can't say it for him."
"In any case, it will be a good sporting event, and I hope that it will be a very fair sporting event," Merkel told reporters in Berlin after meeting with Dutch Prime Minister Mark Rutte.
Merkel, who has frequently attended Germany matches over recent years, was invited to Gdansk by Poland's prime minister, Donald Tusk.
Merkel visited the Germany team at its hotel in Gdansk shortly before the tournament started.
"She seems to bring us luck," Germany midfielder Sami Khedira told reporters in Gdansk on Wednesday.
Coach Joachim Loew's German team beat Portugal, the Netherlands and Denmark in the first round.
The Netherlands' Rutte said he had congratulated Merkel on archrival Germany's performances so far.
"On Sunday, all of Holland crossed its fingers for Germany" against Denmark, he said. "Unfortunately, that didn't help our team — but that's how it is in sport, and of course we wish Joachim Loew and his team success."
Germany, unlike neighboring France, has not said its officials would boycott matches in Ukraine to protest the treatment by authorities there of jailed opposition leader Yulia Tymoshenko.
Merkel, however, didn't go to any of Germany's opening-round matches, which were played in Ukraine.
