The Flying Eagles could not be faulted for effort but were unable to create any clear chances in Christchurch.
Germany scored the winner after just 19 minutes when Levin Oztunali drove home a left-footed shot from the edge of the box.
Nigeria, runners-up in 1989 and 2005, tried in vain to fight back after the break.
Germany will now face Mali in the quarter-finals on Sunday in Christchurch, which is when Senegal will play Uzbekistan in Wellington.
Nigeria have been knocked out of the Under-20 World Cup by Germany, who were 1-0 victors in their Round of 16 clash.