The singer and son Sean were accused of assault after they were refused access to a private event on New Year's Eve, according to a police report.
Sean, 41, allegedly shoved the security guard and Sir Rod, 76, struck his chest "with a closed fist", the report said.
The pair have entered guilty pleas to a misdemeanour count of "simple battery".
It means neither will go to court, nor will they go to jail, pay a fine or go on probation, Sir Rod's lawyer Guy Fronstin said.
The judge withheld adjudication - meaning they have not been formally convicted.