"Dwight is an extraordinary athlete and has incredible athletic ability, but basketball is a game where the most important muscle that you use on the court is the one between your ears," Abdul-Jabbar said on ESPN's "First Take" Thursday. "Dwight's basketball IQ is not up to speed for him to be a dominant player.
Howard, who signed with the Rockets this offseason after a disappointing stint with the Lakers, fired back.
"You can't win three Defensive Player of the Year trophies and be stupid. That can't be done," he said, according to the Houston Chronicle. "And I don't think any coach that has ever coached me has said I have a low IQ for basketball.
"Have I done some dumb stuff on the floor? Yes, every player has. Have I done some stupid things in life? Yes, it's life. We make mistakes and learn from them. It is what it is. I think I am very intelligent when it comes to the game of basketball. I have been playing since I was 3 years old. Each year, I get a little smarter.
"People will have something to say. Is what it is. I'm in (Houston) now. This city has my back and we are going to ride together."
Howard is a seven-time All-Star who has averaged 18.3 points, 12.9 rebounds and 2.2 blocks in his nine-year career, all but one of the years with Orlando. He's made one appearance in the Finals, losing to the Lakers in 2008-09.
Abdul-Jabbar averaged 24.6 points, 11.2 rebounds and 2.6 blocks in a 20-year Hall of Fame career that included six championships. Howard was thought to be the next great Lakers center, but injuries and inconsistency led to Los Angeles losing in the first round of the playoffs.
"When I joined the Lakers I was the greatest center. When I left, I was the worst," Howard said, according to the Chronicle. "Mentally, I wasn't capable of playing center. I understand a lot of things are said out of emotion. I will say if he has anything to say, I am here in Houston. We can talk man to man. That's how I feel."
Howard said he had one conversation with Abdul-Jabbar in Los Angeles and asked that they don't talk about basketball.
"There is no need for me to go back and forth with him," Howard said. "One thing I would say is that he is old enough to where whatever I do shouldn't even matter. He is Kareem Abdul-Jabbar. If I'm Kareem, I'm like why? Four championships, five championships, whatever. I've been in Airplane and done movies with Bruce Lee. I am not worried about the young whippersnapper.
"I wish him good luck. People do things different and when I am done playing, I will do what I can to help the younger generations."