Obama's stance came in an interview with the New Republic, published on Sunday, where he was asked how he squares his love of the game with rising awareness of the impact of repeated head injuries on football players.
"I'm a big football fan, but I have to tell you if I had a son, I'd have to think long and hard before I let him play football," said Obama.
"And I think that those of us who love the sport are going to have to wrestle with the fact that it will probably change gradually to try to reduce some of the violence."
San Francisco 49ers coach Jim Harbaugh was dismissive of Obama's comments.
"Well I have a four-month old, almost five-month old son, Jack Harbaugh, and if President Obama feels that way then there will be a little bit less competition for Jack Harbaugh when he gets older," he said.
Brother John Harbaugh, coach of the Baltimore Ravens, the other team in Sunday's Super Bowl, said he didn't agree with Obama and stressed the game had much to offer.
"Football is a great game ... It's challenging, it's tough, it's hard. There is no game like football. It's the type of sport that brings out the best in you. It kind of shows who you are.
"I think it's a huge part of our educational system in this country. And it's going to be around for a long time," he said.
The 49ers' outside linebacker Aldon Smith said players were well aware of the risks involved.
"I think the game has been like it always has. It's a physical game. Everybody plays hard. Guys get hit sometimes and that's what we all know coming into the game.
"We all signed up for it. It's not like we signed up and thought we were going to play tennis," he said.
Concerns over the risk of brain injury from repeated concussions suffered by players in the NFL are growing with hundreds of former players involved in legal action against the league.
The NFL, America's most popular television sport and a $9 billion a year industry, has introduced tougher rules and regulations regarding the treatment of concussion.
Ravens center Matt Birk said he understood Obama's concerns and felt the game was beginning to change.
"I have three sons and I think anyone who is a parent can relate to that. Certainly it is a dangerous game and we're finding out more and more, every day, the long-term effects that this game can have.
"I think it's a joint effort with the (NFL) commissioner, with coaches, with players, with everybody, everybody that wants to watch and make this game as safe as it can be. I think we're making strides in that," he said.
San Francisco cornerback Tarell Brown agreed.
"It's definitely a dangerous sport, but at the end of the day the league is doing a great job of putting in place things to help players with safety," he said.
"I can understand where President Obama is coming from ... but at the same time the league is doing a great job of preventing a lot of those things."
