This is the weakest growth since quarterly records began in 1992, but some analysts see signs of a recovery.
Growth was 6.8% in the last quarter of 2008, but the first quarter GDP figure dropped as exports fell 17% in March.
China's government has said it is determined to achieve annual growth of 8%, and to expand its domestic demand.
"There's little the Chinese government can do to help key markets for Chinese products in the US and Europe recover," said the BBC's Chris Hogg in Shanghai.
"That's why it's focussing on trying to stimulate domestic demand."
There has been a recognition among Chinese state officials that too sharp an economic slowdown could lead to growing unemployment and may fuel social unrest.
'Pressure'
Announcing the GDP figure, the National Bureau of Statistics (NBS) said that export demand had dropped sharply, cutting into company profits, reducing government revenues and raising unemployment.
"The national economy is confronted with the pressure of a slowdown," an NBS statement said.
China experienced double-digit growth from 2003 to 2007, and recorded 9% growth in 2008.
Analysts said the first-quarter drop in growth was in line with expectations.
But other data offered by the government suggested a tentative recovery may already be under way.
Industrial output expanded 5.1% in the first quarter. It was up 8.3% year-on-year in March, against 3.8% in January and February.
Fixed asset investment on items such as new factories and equipment was up 28.6% in March from 26.5% in February.
Spending on property development grew by 4.1% in the first quarter, and retail sales remained strong with a 14.7% growth during March.
'Surge in investment'
"Most of the indicators are better than earlier market expectations, although the annual GDP growth in the first quarter is a historical low," said Xing Zhqiang, analyst at China International Capital Corporation in Beijing.
"We expect that the most difficult time for China's economy has passed, as the surge in investment has partly offset the negative impact from declining exports."
China has started to implement a 4 trillion yuan ($585bn, £390bn) stimulus package to counter the impact of the global slowdown, and this package has been seen as helping to spur lending in the first three months of the year.
"The overall national economy showed positive changes, with better performance than expected," the NBS said.
It said that urban per-capita incomes were up 11.2% from a year earlier in real terms and that rural per-capita incomes were up 8.6%.
The consumer price index (CPI), China's main gauge of inflation, fell 0.6% in the first quarter of 2009 from a year earlier, according to the bureau.
