The Real Madrid attacker picked up a knock in the opening stages of the Spanish side's 2-1 La Liga win over Levante on Sunday, and was taken off at half-time as a result of his problem.
"He's dizzy. In the first half he was unable to see properly with that eye, but during the break he couldn't see properly with either," commented Madrid coach Jose Mourinho on Ronaldo's injury.
"So it was impossible for him to continue. When he gets to Madrid he will go to hospital to have the tests he needs."
The prolific goalscorer has opted not to take any risks and will remain in Madrid to recover rather than represent the national side this midweek.