Police spokesman Frank Soika said that it was a tradition among employees of the firm to buy sandwiches for each other.
An untouched roll was flown to a Berlin laboratory. Test results confirmed overnight that the free sandwiches had been sprinkled with rat poison, Mr Soika said.
"We don't believe the amount of poison used would have been deadly, but it could have caused serious illness," he said.
Police have launched an investigation and interviewed some of the affected workers, but have no indication yet of who left the poisoned sandwiches or why.
The hospitalized workers are due to be kept under observation in hospital, the spokesman said.
Helmut Kohake, managing director of Mueller Technik, told a press conference on Wednesday that there had been no problems with staff, and no-one had been made redundant.
The firm would be looking at protection measures, which might include fencing off its premises, he said. Employees were upset after the incident, he added. "You don't know whether something like this could happen again," Mr Kohake said.
Mueller Technik, which was founded in 1984 and makes plastic parts for use in cars, has 240 employees.