Mr Balls, who is married to fellow Cabinet minister Yvette Cooper, said that the incident happened last Sunday when they were driving south with their children.
"Although our car has hands-free, I took my phone off the cradle because I did not want to wake the kids," he said.
"We got waved down by a police car almost immediately. I had no points on my licence and accepted the fine and three points without complaint.
"I 100% support the law on mobile phones - it's there to protect the safety of all drivers, passengers and pedestrians."