The suspect placed several tainted items on shelves in various Friedrichshafen markets last week.
These were seized by police and five glasses of baby food were found to contain ethylene glycol, said German media.
Police said the man has remained silent so far but they have found evidence linking him to the incident. However, they cannot give a definite all-clear regarding potentially tainted food.
Authorities received more than 1,000 calls and emails of which 300 helped the investigation.
Ethylene glycol is a clear, colourless, syrupy (viscous) liquid which has a sweet taste but is poisonous if ingested, according to the Centers for Disease Control and Prevention (CDC).
It is used in automotive antifreeze, hydraulic brake fluids, some stamp pad inks, ballpoint pens, solvents, paints, plastics, films and cosmetics.
The extortionist threatened in a letter sent to various people including police that if demands are not met he will put unspecified products contaminated with a toxic substance in various stores in Germany and abroad.
The Ministeriums für Ländlichen Raum, Verbraucherschutz Baden-Württemberg and Polizeipräsidiums Konstanz issued the warning about the potentially contaminated food.
Staatsanwaltschaft Ravensburg and the Konstanz police department are investigating.
They said it doesn’t just affect foodstuffs in a glass jar with a screw-on lid but could involve those in other packaging.
Authorities added lids of properly closed glass jars usually have a curvature inwards and a cracking sound can be heard during opening.