The Germans advanced through Group B with three wins from three games but are bracing for a much tougher defence than what they faced against Portugal, Netherlands and Denmark.
Greece conceded only five goals in 10 qualifiers, though they also let in three goals in three Group A games, advancing as runners-up behind the Czech Republic.
"We got a small taste of what we can expect when we faced the Danes," said Germany holding midfielder Sami Khedira of their 2-1 victory on Sunday.
"Greece are a very compact team, tactically very strong, well organised and aggressive. They are also fast on the breaks and if you see that they had three or four chances in the tournament so far and scored three goals you can tell they are masters of efficiency.
"So patience will be necessary from our side. We have to move because if we remain static it will be very difficult against them. We have to wear them out, tire them out and keep moving."
Germany have yet to find the form that took them to third place in the World Cup two years ago but they have shown they have matured into a team who may lack spark but can be equally effective when it comes to winning games.
"We are calmer now, more clever and we keep our composure for longer," said Khedira when asked to compare this team with that of two years ago. "We are more concentrated over 90 minutes," he said.
The Germans, who will have defender Jerome Boateng back after missing the last game through suspension, will meet either England or Italy in the last four should they advance against the seemingly weaker Greeks.
Asked whether he was happy to have avoided a potential match-up with world and European champions Spain in the semi-finals if they beat Greece, Khedira refused to speculate.
"Our focus is only on Greece because you know surprises happen in football."
German Chancellor Angela Merkel, a fervent supporter of the team, will be hoping there are none as she attends the game but her presence could trigger the ire of Greek fans, angered by Berlin's backing of an austerity plan for the debt-ridden nation.
Both teams have played down the political connotations of the game and Greece will be looking to cause an upset only on the pitch, even without suspended captain Giorgos Karagounis.
Greece coach Fernando Santos has yet to reveal who will replace the inspirational midfielder but it is likely to be Grigoris Makos, a more defensive player, who will try to break up German attacks early.
"There is an atmosphere of self-sacrifice in this team," said midfielder Kostas Katsouranis. "All 11 players will give it all we have got. We have been successful as a team where each one player plays for the team, and that is what we will do again."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.