A Delta airlines worker is seen as luggage is loaded onto the plane at the Fort Lauderdale-Hollywood International Airport in Fort Lauderdale, Florida.

Starting Monday, many airlines around the world begin enforcing a new rule that forbids passengers from checking or carrying on "smart luggage" with non-removable lithium batteries.

Technology-powered luggage began appearing on the market a few years ago, and some new versions of these high-tech bags can do a range of things: They weigh themselves, report their locations, provide power and Wi-Fi signals for gadgets, offer rides to the gate and even follow travelers around.

But while those extras are enticing, there has been industry-wide concern over lithium batteries igniting and starting fires. Last year, the FAA said that lithium-ion batteries were sparking airplane fires once every 10 days on average.

It led the International Air Transport Association to instruct its almost 300 airline members to slap restrictions on lithium-powered smart bags.

As of January 15, "baggage with removable installed Lithium batteries ("smart luggage") must be carried as carry-on baggage or the battery must be removed," the IATA said. "With the battery removed the bag can be checked-in. If the battery cannot be removed, the bag is forbidden for carriage."

Back in December, American Airlines was among the first to alert its customers to the impending rule change, citing "safety management and risk mitigation." The carrier also said the standard questions it asks customers checking bags ("Have you packed any e-cigarettes or spare batteries for laptops, cellphones or cameras?") would be altered to include smart bags.

Other airlines are changing their check-in and boarding procedures as well.

"Throughout our guests' journey, we will remind them to remove all lithium batteries from checked luggage, or disconnect and turn off batteries being stored in the overhead bins," Alex Da silva, a Hawaiian Airlines spokesman told CNBC.

With airlines enforcing the new rules, some smart luggage manufacturers are scrambling to redesign their product, while others are making sure customers know how the lithium batteries can be removed from their bags. Meanwhile, companies that have smart bags without lithium batteries are touting that feature.

"We believed that there would come a time when lithium batteries could be seen as a safety issue. So we purposely powered our luggage with AAA batteries to avoid any of these potential future rulings," Emran Sheikh, President and CEO of luggage manufacturer and distributor Heys International, told CNBC.

Sheikh and others emphasize that it is the type of battery used in some "smart" luggage designs that is the problem—but not the entire category of 'smart luggage' generally.

"Consumers can expect to see luggage manufacturers respond accordingly and release new iterations of smart luggage featuring even safer power sources," said Michele Marini Pittenger, president of the Travel Goods Association.

—Harriet Baskas is the author of seven books, including "Hidden Treasures: What Museums Can't or Won't Show You," and the Stuck at the Airport blog. Follow her on Twitter at @hbaskas. Follow Road Warrior at @CNBCtravel.