The nation's industrial output plunged a sharp 1.1 percent last month, the government reported yesterday, marking the first significant impact of the recession on overall production levels.

Although two-thirds of the drop stemmed from shutdowns in the auto industry, there were sizable declines in virtually every major sector of the economy. The plunge was the steepest since last April, following the Teamsters' strike.

The figures came as, separately, the bulk of the nation's major banks raised their prime lending rates to 13 percent, following the lead of Chase Manhattan Bank of New York, which boosted its rate on Wednesday.

The increases, which had been expected, reflected a continuing push by the Federal Reserve Board to raise interest rates further in order to dampen business loans demand and hold back the growth of the money supply.

However, some analysts fear that if interest rates climb much further it could begin to crimp the economy. The prime has been rising steadily for several months, following a surge in business loan demand.

The drop in industrial production followed two months of lackluster, but not negative, performance. According to revised figures, the index edged up 0.1 percent in July and remained unchanged during June.

The August figures were depressed by a sharp 15 percent drop in auto assemblies, which in turn led to declines in production of raw steel, textiles and other auto-related supplies.

Auto assemblies fell to an annual rate of 7.5 million units, well below the 8.9 million-unit pace of the first half of the year. Automakers have been plagued by an excess of inventories, brought on by the gasoline shortage.

However, declines were posted throughout the economy. Output of consumer goods fell 2.1 percent last month, while production of business equipment dipped 0.8 percent, and intermediate products edged down 0.2 percent.

The only major area not to show a decline was in construction supplies, where output rose a scant 0.1 percent. Within the consumer goods category, durables plunged 5.4 percent while nondurables fell 0.7 percent.

Yesterday's report brought the overall industrial production index to 150.9 percent of its 1967 average -- 1.4 percent below its peak level last March and only 2 percent above its mark a year ago.

The Federal Reserve Board, which publishes the index, said automakers tentatively have scheduled an increase in their production for September, but Ford Motor Company recently announced some temporary shutdowns.