Days after a military coup on 11 September 1973, around 12,000 suspected leftists were rounded up and herded into the National Stadium, which was used as an interrogation and torture centre.
The viral campaign, #goldesilencio (silent goal), which quickly trended on Twitter, is ran by human rights campaigners Amnesty International.
A video uses footage of the time with words superimposed saying: "To all Chile's players we want to ask that when the first goal arrives - don't shout.
"Keep down in your throat that shout that comes from the soul. Squeeze your fist so your hand doesn't raise to the sky. And if you really want to celebrate, make the stadium quiet."
The upcoming 40th anniversary of the coup has led to deep soul-searching in Chile, where some 3,000 people "disappeared", presumed kidnapped and killed by the military, in the 17-year dictatorship that followed.
Those who lost their lives include the Chilean singer Victor Jara, who, according to witnesses, had his hands battered with a revolver before being shot dead in another football stadium.
His family filed a lawsuit on Thursday against the former army officer they accuse of the killing.