Kubica, 22, rolled twice at the Casino hairpin after Jarno Trulli's Toyota forced him off-line, causing his car to become airbourne and then smash into a concrete wall.
Initial fears were that Kubica had broken his leg, but his team later confirmed that he had only suffered a sprained ankle and concussion.
Following his transfer from the circuit medical centre to the Sacre Coeur Hospital in Montreal, a statement was released by doctors.
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"Mr Kubica has undergone all the necessary medical examinations and we don't foresee any further treatment will be required following the accident," read the statement.
"He is suffering from a light trauma to his brain as well as a sprain on his left ankle.
"His condition is therefore judged to be stable and we don't have any fear for his life. Mr Kubica will remain in hospital and his state of health will be re-evaluated tomorrow morning."
Kubica's injury means that it is highly likely the second car will be raced in the USA by either one of the team's German test drivers Sebastian Vettel or Timo Glock.
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