The Argentinian Rugby Union (UAR) have not officially confirmed that the player will miss the tournament in September but his participation now seems to be highly unlikely.
"This is a terrible blow for us," team captain Agustin Pichot told the newspaper La Nacion newspaper.
"We are angry and sad. If there was a guy who deserved to play the World Cup, it was him.
"There are not too many things to say. I only hope Martin gets over it soon."
His sentiments were echoed by full-back Ignacio Corleto, who added: "The squad is shocked, but we only want him to get over it.
"This is like a bomb. As happens in life, you have to fight until the end.
"We have to get over this shock. If Martin can, we can."
This not the first time that an Argentine player has suffered such a problem after second row Alejandro Allub was forced to retire following a similar incident during a tour to New Zealand in 2001.
"There are no causes you can predict," said team doctor Mario Larrian.
"What has happened is quite rare as, according to statistics, it happens to one in six million people. Unfortunately, it has happened to us twice."