South Yorkshire Fire & Rescue said the crew were called on Wednesday to free the youngster who had gotten trapped in the seat designed for babies and toddlers at a playground.
The incident followed a rising trend on TikTok where users film their friends being freed from the tiny swings for a video.
But the fire service described the trend as "not funny", and called on parents to make their children aware of the seriousness of wasting emergency services' precious time and resources.
Posting on their Facebook page, the service said: "Yesterday we were called to rescue a young person who was trapped in a baby swing...
"We believe this was a direct result of a TikTok challenge that has been doing the rounds in recent weeks.
"Now, whilst we're in support of children getting out in the fresh air, we cannot support this particular challenge - this incident wasted our time and could have slowed our response to a serious incident.
"Please, if you know someone who's taking part in this challenge, ask them not to. This one isn't funny!"
Support The Yorkshire Post and become a subscriber today. Your subscription will help us to continue to bring quality news to the people of Yorkshire. In return, you'll see fewer ads on site, get free access to our app and receive exclusive members-only offers. Click here to subscribe.