The man, Darcy Pell, said he was "not a hero - just saw a dog in need" after he took the plunge at around 12.30pm today (Saturday).
He can be seen smashing through the ice in Pontefract Park lake before grabbing hold of the dog, which appeared to have fallen through the ice and was stuck.
He then swims back to the edge of the lake with the dog before handing it over to its owners.
Passer-by Paula Town posted footage of the rescue online, saying: "What a hero, this complete stranger rescued this family's dog when it got into trouble in Pontefract Park."
She told the Yorkshire Evening Post: "When we got to the lake, I could see a dog in the water, it was trying to get onto the ice but kept falling back in.
"I felt panic-stricken and scoured the side of the lake for a life buoy but couldn't find one.
"Luckily that guy came along, he lowered himself into the water and the rest is on the video."
Mr Pell, 31, was out on a run with a friend when he spotted the stricken animal, believed to belong to a man and a woman also in the video.
After his heroic rescue, Mr Jarvis's friend gave him his jacket and they carried on their run.
Mr Pell stressed that he was an experienced cold-water swimmer and advised others not to copy his actions as it could be dangerous.
Mr Pell, who is from Cardiff but lives in Doncaster, wrote on the Pontefract Community Page: "Not a hero just saw a dog in need. Luckily swim in cold/icey water as a hobby and know the risks it can cause. Carried on my run after so no big deal. Was given a jacket by my run buddy. Obviously wouldn't recommend people doing the same.
"Just glad the dog was happy to carry on its walk after."