Karunas, who has recently come in for flak on social media for supporting AIADMK chief V K Sasikala, arrived to garland a statue of freedom fighter Pasumpon Muthuramalinga Thevar when the incident occurred, police said.
The footwear fell on the car, police said adding they were investigating to trace the culprit.
There were reports that a section of the people in his constituency was not happy with his decision to support the Sasikala camp after former chief minister O Pannerselvam revolted against the leadership.
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