The Inter Milan player pulled up with hamstring trouble towards the end of Sunday's opening Group C match.
The 27-year-old went for medical tests as the rest of the squad trained on Monday and doctors later confirmed a hamstring injury.
"The imaging results found an injury to his hamstring, which rules him out of participating in the rest of the tournament," a Uruguyan Football Association statement said.
Uruguay boss Oscar Tabarez admitted during post-match press conference that he had been worried about the extent of Vecino's injury.
Tabarez said he had been planning give Luis Suarez a few minutes' rest when he was forced to send on Real Madrid's Federico Valverde for Vecino with the game winding down.
Suarez had earlier notched his 57th goal for Uruguay.
Uruguay face Copa America newcomers Japan in their next match on Thursday, which may provide a chance for either Valverde or Arsenal's Lucas Torreira to stake their claim to a regular spot.