The man, 65, was walking in woods near the town of Buchen when he encountered the female African elephant, called Baby.
The 34-year-old elephant was later captured and returned to the circus.
Police are now investigating how the elephant got out of its enclosure and why it acted so aggressively.
"There's evidence of third-party involvement," Heidelberg police spokeswoman Yvonne Schmierer told the AP news agency.
"Either someone forgot to shut the enclosure, or the elephant was released intentionally."
Local news agency Stimme reported that the elephant had previously injured at least two people - including a man who was thrown in the air and a 12-year-old boy who suffered a broken jaw when he was hit by its trunk.
Stimme reported that the German branch of animal rights group Peta was urging the authorities to remove the elephant from the circus.
A man taking his regular morning stroll in south-west Germany was attacked and killed by an elephant which had escaped from a circus, police say.