Cherry ripped Burke during his Coach's Corner segment on Saturday's night "Hockey Night In Canada" broadcast.
He called out Burke on various issues, from not having enough Ontario-born hockey players on the Leafs to attempting to get Cherry fired from the CBC.
"Every team in the National Hockey League has a guy from Ontario except one — it's Ontario's Toronto Maple Leafs," said Cherry.
"If you want Americans, you got the team. It's the only organization in Canada that cheers when Canada loses and it's an absolute shame.
"There's 40,000 kids in the GTHL ... (Tyler) Seguin, (Jeff) Skinner, (Jason) Spezza — they all come from the GTHL. This guy (Burke) has none. He has all Americans, he has American college guys who play for him right now and I could go on and on."
Cherry's rant comes a day after Burke fired Leafs coach Ron Wilson and replaced him with former Anaheim Ducks coach Randy Carlyle, who was born in Sudbury, Ont.
Burke had complained in the past that Cherry was being too critical of Wilson during his CBC segments.
"Here's what kills me — Burke goes to my bosses and says I'm a bad guy and I said something 'vicious' about his coach," said Cherry. "Two weeks later he fires him. Figure that one out folks."
Cherry listed various NHL teams and counted the amount of Ontario-born hockey players on each one. Vancouver (four Ontario-born players), Pittsburgh (six), St. Louis (nine) and Boston (nine), he listed as examples.
"And here's another thing that bugs me. We pay his salary from Ontario. We are the fans from Ontario. We are the only ones who would put up with going four years ... to not make the playoffs three years, probably not four, and not have one guy from Ontario, that's a crime as far as I'm concerned," Cherry said.
Cherry, who made news recently when he joined social media site Twitter, became more animated as the broadcast went on, challenging Burke to come after him and his job.
"If he wants my job, if he wants to get me fired, like he tried to do, go behind my back with my bosses and try to get me fired," he continued, "not only that he went to the governors and said it too. You want to get me off? You want to take me on? 'Oh Brian Burke, I'm shaking in my boots.'
"Do your best."