Authorities have urged the public to be vigilant about signs of tampering, releasing a surveillance camera image of the suspect, a man aged around 50 wearing glasses and a white cap.
To press the demand, the blackmailer poisoned five baby food products and last week alerted police to the store they were placed in, in the southern city of Friedrichshafen on Lake Constance.
"We take this threat very seriously," said chief prosecutor Alexander Boger in a televised press conference.
The blackmailer had demanded 10 million euros (USD 12 million) from a retail chain, reported Bild daily. The threat was made in an email that was also sent to a consumer protection group and police.
It did not specify which type of food would be poisoned, or in which region or stores the products would be placed.
A state consumer protection ministry official said the substance detected was ethylene glycol, used in anti-freeze products and brake fluids, which is toxic, and fatal in large quantities.