The frightening incident happened in the area of the Lido in Stenhousemuir.
A man, who was sitting on a bench, took hold of the arm of the child as she walked past with her mother.
He appeared to be drunk and his actions caused alarm to both the child and her parent, so police were contacted.
Officers attended and are now following a positive line of inquiry to trace the man in question.
A Police Scotland spokesman said: “While these types of incidents are concerning for the public, it is important to stress that this was not an attempt to harm the child in any way, rather actions on the part of the male that were ill considered.”
The incident happened at around 2pm on Wednesday (April 20).