FRANKFURT — The economic stagnation in Europe has taken a significant toll on Germany, with government figures released Tuesday showing that the Continent’s flagship economy contracted in last year’s fourth quarter.

The Federal Statistical Office in Wiesbaden estimated that the German economy shrank about 0.5 percent in the final three months of 2012, compared with the previous three months. The decline was largely the result of sagging investment by German managers worried about the future of the eurozone.