The assault occurred Monday outside a shop in the Helsingborg, TT reported.
The teenagers were kicking a dog when the woman intervened. The gang then punched the woman in her face and she fell to the ground. The boys then kicked her until she started bleeding.
The woman managed to make her way home where she was bedridden for days.
Now, a man who wished to remain anonymous has offered the $4,000 reward to help police catch the culprits, the local Helsingborgs Dagblad newspaper reported.
"I have told him that if he wants to do this, that is perfectly fine. It will surely lead to some unreliable tips but we'll make assessments," said Torsten Persson of the Helsingborg police.
Persson said it is very unusual for members of the public to offer cash rewards.
"I have experienced it a few times, but usually it is relatives who are prepared to pay," he said.