The 31-year-old has been diagnosed with mild concussion after he was hit on the head during the Proteas' second innings on Saturday, in which Johnson took 5-59 to lead his side to a crushing 281-run defeat of the hosts in Centurion.
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McLaren was dismissed by Johnson soon after taking the blow, and on Tuesday Cricket South Africa confirmed that he will play no part in the second Test in Port Elizabeth - which starts on Thursday.
"Ryan was admitted to Johannesburg Clinic on Sunday evening suffering from suspected concussion-related symptoms including worsening headaches and nausea, which started approximately 30 hours after the blow to his head," said team manager Dr Mohammed Moosajee.
"His condition improved overnight and he was re-assesed by a neurologist as well as a leading sports physician with a special interest in concussion, Dr Jon Patricios.
"He is doing much better and has been discharged but from a medical protocol point of view, any form of concussion is concerning enough to rule him out of the next Test match.
"He will be monitored over the next four to five days and will have further assessment done next week Monday to decide whether or not he can join up with the squad priot to the third Test in Cape Town."
Cricket South Africa confirmed that they would not be calling up any cover into the squad for McLaren, who made 14 runs and contributed match figures of 2-119 on his return to the Test side after a four-year absence.