Suarez, who helped Uruguay to fourth place at the last World Cup in South Africa four years ago, will need 15 to 20 days to recover but Uruguay team doctors are not ruling him out of the tournament in Brazil, which runs from June 12 to July 13.
"Many thanks to all of you for your support. Relax, because I'll get there and work hard these days to be 100 percent to help my team mates," Suarez said on the local sports website ovaciondigital.com.uy.
The Liverpool forward went under the knife on Thursday morning after an MRI revealed a meniscus injury in his knee, suffered in training with the national team.
The South American's first match is against Costa Rica on June 15 before they face England in Sao Paolo on June 19.
"Yesterday, Wednesday 21st of May, Luis Suarez suffered an intense pain in his left knee after an undergoing a normal warm up," said a statement from the Uruguay Football Association (AUF).
"He had an MRI scan which confirmed a partial lesion of the external meniscus of his left knee.
"On Thursday morning, he underwent an arthroscopic partial resection of his meniscus in the Medica Uruguaya hospital (Montevideo).
"There was no evidence of any further damage to the knee.
"His participation to the World Cup in Brazil has not been ruled out."
Recovery time tends to vary from player to player, but typically varies from two to six weeks, which could put the Uruguayan’s World Cup participation in doubt.
Bookies have responded by lengthening their odds of escaping from a tough group stage - which includes England, Italy and Costa Rica - to 1/2.
Luis Suárez HAS injured his knee & will have minor op today. My source in Uruguay tells me he will miss #CRC game but could face #ENG
Uruguay play Costa Rica on June 14th, England five days later on the 19th, then face a potentially crucial final group stage match against Italy on June 24th.
It seems that even if Suarez recovers in time, he will certainly be short of match fitness.
That leaves Uruguay in trouble since their other top striker, Edinson Cavani, has suffered a severe drop-off in form since going through a messy divorce in January.
A positive prognosis was also put forward by the player’s mother, who was quoted as saying that Suarez’s injury “wasn't as serious as we thought”.
"Thank God everything went well. What Luis had wasn't as serious as we thought," Suarez's mother, Sandra Diaz, told @AP
Suarez netted 31 league goals for Premier League runners-up Liverpool this season and was expected to be one of the stars in Brazil, though Uruguay’s chances of progressing out of a group that includes England, Italy and Costa Rica will take a significant hit if he is unable to return to full fitness.
Ben Dinnery, a trained physio and expert for Physioroom.com, said: “If the reports are true and his MRI results did in fact reveal a minor meniscus tear then it’s likely that he will have an operation known as a partial meniscectomy which will remove the torn cartilage.
"This procedure is particularly effective for small tears which affect the mechanical function of the knee; straightening, clicking or locking and the prognosis is good in both the short and long-term.
"Typically patients can expect a return to normal activity within one month although strenuous exercise may be restricted. Without knowing the full extent the injury, it is difficult to predict an accurate timescale for his recovery, but it is more likely he will be targeting the Italy game on June 24th (33 days’ time).
"Chilean international, Arturo Vidal, underwent an almost identical procedure at the beginning of May and was recently passed ‘fully fit’ by the Juventus and Chile medical team, so at this stage its realistic that Suarez will still play a part in the tournament.”
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