The powerful right hook was captured by local television station 8 Andalucía during the procession staged by the Brotherhood of San Sebastian.
The aged victim of the attack received emergency treatment after the incident, the station reported.
"Let's hope that's the final incident in these celebrations which are supposed to be shared and enjoyed peacefully," the presenter said.
Video of the incident during the Easter procession from Spanish TV channel 8 Andalucía.
Twitter users also expressed their outrage.
El que le ha pegado el puñetazo al hombre ese en San Esteban no lo ha matado de milagro. Que dé gracias a Dios por que no lo hayan linchado.— ale gomez (@alegomez777) April 16, 2014
It's a miracle the guy who threw the punch didn't kill him. He should give thanks to God he wasn't lynched," wrote Twitter user Ale Gómez.
Local daily Diario de Sevilla reported the attack had not been an isolated incident on the day known as Martes Santo, or Holy Tuesday.
"Too much sun? Or a simple lack or manners?" the paper asked its readers.
Seville's Holy Week, or Semana Santa, celebrations are world famous, drawing thousands of tourists, and are an integral part of the city's social and cultural life.
The processions — sometimes lasting up to 14 hours — involve elaborate floats and the participation of large music bands and hundreds of penitents, or nazarenos wearing distinctive conical hats.