The injury was at first thought to be relatively minor, incurred during the fourth minute of Monday's 4-0 friendly victory over South Korea.
"He had a knock on his left thigh," said team doctor Baba Adam.
"We initially tried to see if he could go back to play but we realised it was an injury that needed to be taken care of and managed well.
"We did an MRI on the quadriceps and what we realised is that, there was a tear.
"We hope to get him on to the field again pretty soon. However, we are still monitoring him to the deadline when we will give our final statement on his state of affairs."
Waris' absence would be a huge blow after the diminutive attacker played an integral part in Ghana's qualification for Brazil, during which he scored three goals.
"The Fifa deadline is (June) 15, so we will monitor until that day and see how things turn up," said Adam before adding that Waris is improving and "can now bend his knee with little pain."
Ghana begin their World Cup campaign against the United States on Monday before meeting Germany on June 21 and Portugal on June 26.