Liverpool striker Suarez had keyhole surgery on his left knee on Thursday (local time) and faces a race to be fit for the World Cup in Brazil, where Uruguay play Costa Rica in their opening Group D game on June 14 and England in their second match on June 19.
Suarez complained about the problem during his first day of training with the Uruguay squad.
The country's FA (AUF) said he first suffered the injury in the final Premier League game of the season at home to Newcastle as Liverpool chased the title.
Dummett was sent off for fouling Suarez late in the match.
"It should be highlighted that the player received a direct blow to his left knee in the last game of the Premier League season with Liverpool, on Sunday May 11, with pain which eased with rest from sporting action after the season had ended," the Uruguayan FA said on Thursday.
Dummett, whose red card in the 82nd minute of Newcastle's 2-1 defeat was later rescinded on appeal, was the victim of death threats on social media from local fans as the AUF seemed to blame Newcastle for Suarez's operation.
The 22-year-old Newcastle defender, who was called up by Wales on Thursday for a friendly against the Netherlands on June 4, has referred the threats to football authorities.
Suarez will need up to 20 days to recover but Uruguay team doctors have not ruled him out of the June 12 to July 13 finals.
"The challenge was inadvertent. I hit him and the ball with my left foot and he went down under the challenge," Dummett told the Daily Mirror on Thursday.
"I hope he makes the World Cup because he is one of the best players in the world so he should be there.
"Having said that, I injured my meniscus three years ago and I was out for three months, so it will depend on the injury and exactly where it is on the knee."
