The figure was in large part the result of strong domestic demand, official seasonally corrected figures data showed, good news for Germany's traditionally export orientated economy.
The reading also underscored a catch-up effect from the fourth quarter of 2010, which saw growth of just 0.4 percent owing to poor weather.
In the three months from January to the end of March meanwhile, "a positive contribution was made mainly by the domestic economy," a statement issued by the national statistics office said.
It underscored corporate investment in capital goods and a pick up in the public works and construction sectors.
"The pre-crisis level of early 2008 has been exceeded already now," the Destatis office said.
Less than two years ago, economists had estimated that benchmark would not be reached before 2013, but German manufacturing in particular has benefitted from global economic growth since then.
Analysts polled by Dow Jones Newswires had forecast a smaller first-quarter 2011 gain of 0.9 percent, and the sign of domestic strength will be welcome given forecasts of a slowing in foreign demand ahead.
"Germany, 12 points," ING senior economist Carsten Brzeski joked in reference to the maximum score at the Eurovision song contest that takes place on Saturday in Düsseldorf.
On a 12-month comparison, Germany's price-adjusted gross domestic product gained an impressive 5.2 percent in the first quarter, which meant GDP "rose more sharply than ever since German unification" in 1990, the statement said.
Germany continues to post one of the strongest growth rates in Europe, despite headwinds such as the eurozone debt crisis, rising oil prices, inflation and interest rates, and unrest in North Africa and the Middle East.
France reported quarterly growth of 1.0 percent on Friday, already better than the 0.50-percent increase seen in Britain.
"Germany is the growth engine among industrialised nations, and not only in Europe," new Economy Minister Philipp Rösler said in a statement.
The economy expanded by 3.6 percent in 2010, and several economists believe it will add an additional 3.0 percent this year.
At the moment, the official growth forecast from Berlin is 2.6 percent.
"With its sound fundamentals, the economy is heading towards a second Wirtschaftswunder," or economic miracle, Brzeski said.