The 11-year-old victim was watching his team when he was hit by the explosive hurled within the away section.
The boy was taken away by police and paramedics suffering from minor burns which medical staff said could have been “far worse”.
A 16-year-old boy has been charged over the incident and is due to appear at Aberdeen Sheriff Court today.
The victim’s father, who asked not to be named, said his son was also hit with a firecracker during Hearts’ recent match against Celtic.
He said: “He has a couple of marks where it hit but apart from that his legs are okay.
“But if it wasn’t for the fact he was wearing jeans and trainers the medical staff said it could have been a lot worse.
“It happened at Parkhead a few weeks ago when Hearts were playing Celtic – and again it was a Hearts fan who threw it.
“This time it bounced off his feet and hit his leg. I’m glad the police have charged someone.”
The latest incident comes less than two months after a group of young Hearts supporters allegedly pushed a Ross County supporters’ bus driver, stole a County fan’s drum and a steward’s cap.
Hearts also condemned the setting off of flares inside the stadium during the 2-0 win on October 24.
The club said it was also aware of the Celtic Park incident in which the young supporter was injured by a pyrotechnic.
In a previous statement, the club said that a “number of fans” would banned for bad behaviour and promised a “greater stewarding presence” at games.
It also warned that police will be “monitoring certain areas directly” and that the club was looking at introducing much “more strenuous ticketing control measures”.
The club, which has pledged to work with schools and social work departments in a bid to tackle antisocial behaviour at games, added: “We find it incredible that, even following the terrifying ordeal a young Hearts fan had at Celtic Park due to pyrotechnics in our section – an incident that led to him receiving medical treatment – certain individuals still chose to repeat this utterly irresponsible action.”
A police spokesman said: “At about 1.45pm on Saturday we received a report of a pyrotechnic at the Hearts’ game which occurred in the away section of the Pittodrie Stadium.
“An 11-year-old boy received a minor injury as a result of the pyrotechnic and received medical treatment at the ground.
“A 16-year-old male has been cautioned and charged in connection with the incident and is expected to appear at Aberdeen Sheriff Court on Monday.”
Hearts lost Saturday’s league match 1-0.