Liverpool's Uruguay striker underwent an operation in Montevideo where doctors performed an arthroscopic partial resection of his meniscus.
An official reported there were no complications, with Suarez leaving hospital in a wheelchair.
Suarez was quoted as saying: "I'll work quietly and very hard in the coming days to be 100 per cent and help my team-mates."
The 27-year-old later posted a picture of himself with his family on Twitter, with the message: "Thank you very much for the messages of support, love and encouragement throughout the day!
"The strength that my loved ones give me... will make me work hard to reach the World Cup. My family and I are very grateful to all of you!!"
Suarez had an MRI scan after feeling discomfort in his knee during training on Wednesday, with the Uruguay Football Association claiming this was a result of a knock he sustained in the final fixture of the Premier League season against Newcastle.
Uruguay open their World Cup campaign in Group D against Costa Rica on June 14, followed by matches with England and Italy.
Newcastle defender Paul Dummett, who was sent off for making a wild lunge on Suarez, says he has received some menacing abuse from Uruguay supporters on Twitter.
And Dummett, speaking to The Mirror, said: "The challenge was inadvertent. I hit him and the ball with my left foot and he went down under the challenge.
"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."