A group of teenagers were also siting in the back seat.
Waikato police said when the woman was questioned, she appeared to just shrug off the concerns.
Area commander Naila Hassan said the woman didn't appear to show any concern for her son's welfare and the teenage passengers.
"He was on her lap, on the road, with her drunk."
Hassan said it was "shocking, irresponsible behavior that puts everyone's lives at risk on the road".
"This is 5pm on a Sunday - a high risk time, in a high risk location with a three-year-old on her lap. We could have lost a little kiddie."
Hassan said had the patrol car not been there it could have been fatal.
"It's just disappointing that there are still people out there on the roads making such poor decisions - some people just don't get it.
"It's important to remember that even small amounts of alcohol can affect your driving. The best advice is always to make the choice to drink or drive, not both."