German GDP (gross domestic product) grew by 0.4 percent - down from 0.7 percent in 2012 and 3.3 percent in 2011, the Federal Statistics Office (Destatis) said in a statement.
It was the economy's worst performance since the depths of the recession in 2009.
But Economy Minister Sigmar Gabriel said that "even if annual average growth figure looks fairly subdued, it has to be seen positively."
"Germany was largely able to escape the recession that has hit a number of euro-area countries. The German economy is in good shape. All indicators suggest that consumers and companies are counting on a broad-based recovery," Gabriel said.
Destatis President Roderich Egeler said: "Clearly the German economy has been negatively affected by the ongoing recession in some European countries and sluggish global economic growth. Strong domestic demand could only partly compensate for this.
"Nevertheless, after the period of weakness last winter, the economic situation improved through the course of 2013."
Germany has come under heavy fire recently, from both its European neighbours and the United States, for its booming trade surplus, which critics argue has been built up at the expense of the country's crisis-ridden neighbours.
But the latest figures appear to contradict the critics. Domestic demand climbed by 0.9 percent, and it was a poor year for export growth - the cornerstone of Germany's economy - which posted an increase of 0.6 percent compared to 3.2 percent in 2012.
Experts had predicted GDP growth of 0.5 percent for 2013.
In the last three months of the year GDP rose by 0.25 percent.
"The eurozone crisis hurt export-orientated industries, particularly at the start of last year," said Ferdinand Fichtner of the DIW economic think-tank. "But since the spring, GDP has expanded at a moderate pace."
Commerzbank chief economist Jörg Krämer said the German economy "has sustained the solid gain seen in the third quarter."
And rising leading indicators, such as confidence surveys, "suggest that the expansion will probably continue at a similar pace in the first quarter" of this year, he said.
He forecast growth of 1.7 percent for the whole year 2014.
"The German economy is benefitting from the end of the recession in the euro area," he said.
Germany's public finances were also in the red last year, with a deficit equivalent to 0.1 percent of GDP compared with a slight surplus in 2012, the statisticians said in a statement.