It was India's weakest growth for six quarters, but still better than had been expected.
The gross domestic product (GDP) growth figure from the finance ministry compares with the annual rate of 7.8% in the first three months of the year.
The slowdown is expected to continue as India's central bank continues to raise interest rates to control inflation.
The Reserve Bank of India (RBI) has raised interest rates 11 times since March 2010. The next rate-setting meeting is on 16 September, when many economists expect rates will rise again.
Inflation in July was 9.22%, which was well above the RBI's target rate of 4% to 4.5%.
The sector breakdown showed that the construction sector had been one of the worst-performing parts of the economy.
Construction grew at an annual rate of 1.2% in the second quarter, down from 8.2% in the previous quarter, as rising interest rates and delays in planning approvals held up building projects.
Farm output rose 3.9%, which was down from the previous quarter but above the level of 2.4% in the same period last year.
The manufacturing sector grew 7.2%, an improvement from the previous quarter, but well below the 10.6% in the second quarter of 2010.