The 22-year-old attacking midfielder had to come off in the 25th minute of Paraguay's 4-0 win over Nicaragua in Asuncion, with the team's head coach Gustavo Alfaro saying Enciso will undergo tests.
Alfaro said he remained "hopeful" that the injury was not muscular, but the loss of the Strasbourg midfielder, who's impressed in France's Ligue 1 this season, would be a huge blow for Paraguay.
"Julio suffered two simultaneous injuries; a tight hamstring from impact and then on his waist, which affected his quadriceps area," Alfaro said. "He got scared and that's why he came off."
Enciso scored a dozen league goals for Strasbourg and has four goals in his 31 caps for Paraguay as they head into their first World Cup since 2010. The youngster, also shone for Brighton in the Premier League.
"When he took the first hit, he signaled to me and I told him to come off. He replied that it was loosening up, but then he took another blow to the waist and that's when he felt the injury," Alfaro said.
"We hope Julio is all right and he can be ready to return for the opener against the US."
Paraguay, who'll play their group matches in California, face the hosts in their group D opener next Friday in Inglewood before taking on Turkey on June 19 and their last pool match will be against the Socceroos on June 25 at Levi's Stadium in Santa Clara.
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