Both opioid medicines are in some cough and cold remedies, and were commonly prescribed by doctors and dentists despite the risk of life-threatening breathing problems in children.
The FDA also warned nursing mothers who are taking the medications can pass unsafe levels of opioids to their babies through breast milk.
Children and teens ages 12 to 18 shouldn't take them if they are obese, have obstructive sleep apnea or a weakened respiratory system. The risks factors can increase their chances of serious breathing problems, according to the FDA.
The American Academy of Pediatrics strengthened its warnings about prescribing codeine for children late last year, because of reports of deaths.
Dr. Charles Cote, a Boston anesthesiologist and co-author of the report, told the Associated Press that considering other remedies such as acetaminophen and ibuprofen for pain and simple remedies such as ice or popsicles after tonsillectomies are better options.
"Maybe a little pain is better than the alternative," Cote said.