One fan took to social networking to warn “a bullet” would be waiting for Dummett if he ever visited Uruguay.
It comes after Dummett was red-carded for a tackle on the Liverpool striker on the last day of last season.
The red card was chalked off by the FA last week and Dummett was cleared of any wrongdoing.
But Suarez has since undergone an operation on the meniscus in his knee that means he is facing a race to be fit for the World Cup finals, where Uruguay are set to face England in Group D.
The threats came on the same day Dummett was named by Chris Coleman in the Wales squad to face Louis Van Gaal’s Dutch team in Amsterdam on June 4.
They began on Twitter with one follower Federico Gonzalez posting:”Hi Paul Dummett, from Uruguay we hope someday u come here to have a nice time w/ friends.
“We have things for you, like a bullet in the head.”
Another tweeter going by the name of @DjAlvinGreen said menacingly: “Hey, Paul Dummett, if Suárez doesn’t play against England, you’ll never play again. Kisses.”
Dummett himself has stayed silent on the matter while the Uruguayan FA has actually given a statement saying Suarez’s injury was sustained in training.
In a statement the association said on Thursday: “Luis Suárez suffered an intense pain in his left knee after undergoing a normal warm-up.
“The early diagnosis was a stable injury to the external meniscus in the knee. He was examined by a scan, which confirmed a partial injury to the external meniscus.
“This morning the meniscus was repaired via arthroscopy at the Médica Uruguayan hospital. There was no evidence of other injuries to the knee.”