The calculation was in terms of the real buying power of wages, allowing for inflation, and the fall bodes ill for efforts to fire up domestic consumption to boost recovery in Europe's biggest economy.
Germany has relied mainly on exports to drive growth.
Citing preliminary results, the statistics office said that nominal wages in 2013 were up 1.3 percent from the previous year, but that consumer prices rose faster, at 1.5 percent, over the same period.
"One reason for the decline in real wages in 2013 was a decline in bonuses which are frequently performance-related," said a statement by the Wiesbaden-based agency which is known as Destatis.
If such special payments are not included in the statistic, then real monthly wages would have increased by 1.7 percent year-on-year, higher than the rate of consumer price inflation, said the office.