The incident happened on Sunday in the northeastern city of Stralsund in the Vorpommern-Ruegen district. District chief Stefan Kerth said in a statement that he regretted the mishap.
"I deeply regret the incident. This single event is the result of an individual mistake. I hope that all those affected will not develop serious side-effects," he said.
Those injected with the drug were aged between 66 and 82. They were sent home as soon as the mistake came to light. Four developed flu-like symptoms and were hospitalized for observation.
The district authority pointed out that the vaccine's German developer, Biontech, had used higher doses during the first phase of trials and observed no lasting side-effects in the volunteers.