The seasonally-corrected figure from the National Statistics Institute followed a 6.9 percent fall recorded for February in the eurozone's fourth biggest economy.
It was the softest decline since August 2011, just before the latest recession started.
Like February's figure, the March fall was driven by weakening production of durable consumer goods, the institute said.
Production in the capital goods and energy sectors strengthened by 3.3 percent however.
Industrial production had fallen by 4.9 percent in January, 7.1 percent in December and 7.0 percent in November.
In its efforts to strengthen the public finances Spain's conservative government has imposed tough economic reforms that have curbed consumption.
It forecasts the economy will contract by 1.3 percent this year.