The entrepreneur and TV personality, who is reportedly worth of £175 million, said he was stopped by police for using the device in his car while dropping his son at a cricket match.
Writing on Twitter, Bannatyne, 65, said he had been "stupid".
Bannatyne told his 685,000 followers: "Busy day so far. Dropped son at cricket. Got stopped for using mobile phone in car. Missed train. So! Tell me how your day has been so far!!
"I accept it was very stupid of me to use phone in car. Will pay the fine, take the points & won't do it again."
One Twitter user replied: "No excuse for using mobile in car - I'd guess your motor has built in blue tooth. Hope you get 3 points."
Clydebank-born Bannatyne told one follower he had "a short lapse in my brain this morning" and promised not to do it again.