Output at manufacturing firms added 0.3 percent month-on-month, federal statistics authority Destatis said, making good some of June and July's decline.
But with German business racked by uncertainty over US-led trade wars, Brexit, and an emerging market slowdown, production was still four percent below the August 2018 level.
"Industry remains in a downturn," the economy ministry said in a statement, as "weakness in demand is persisting".
Looking to different areas of industry, both producer goods and capital goods makers reported increased output, while consumer goods firms' production fell back.
Figures released Monday also showed industrial orders -- a closely-watched indicator of future activity -- falling in August.
The warning signs have stoked fears for the wider German economy if weakness spreads from the key export-oriented manufacturers to other sectors.
Lower orders and other indicators point to "a bottoming out of industrial production at best" in August, ING bank economist Peter Vanden Houte said.
"A real recovery looks some time away," he added, while "German industry remains extremely sensitive to further developments in the trade war".
US President Donald Trump is expected to decide next month whether to hit cars imported from Europe with tariffs.