Alisson was forced during Brazil's World Cup qualifier against Colombia after clashing with Davinson Sanchez.
He has now been withdrawn from the Brazil squad and flying back to England.
A statement from Liverpool on Friday read: "Alisson Becker has departed the Brazil national team set-up and will return to Liverpool.
"The goalkeeper was forced off in the second half of his nation's World Cup qualifier with Colombia in the early hours of Friday following a collision. Alisson is travelling back to Merseyside and will undergo assessment from the Reds' medical staff."
Speaking after the game, Brazil doctor Rodrigo Lasmar confirmed: "Alisson suffered a head injury. He was replaced due to a suspected concussion, so now we will follow the protocol recommended by the CBF. He will undergo the recommended imaging tests. First, we will perform a CT scan, followed by a diffusion MRI.
"If all the tests are negative and normal, we will then perform a cognitive test, and then we will evaluate the player. If everything is normal, we will conduct a series of observation tests over the next few days to see whether or not he would be able to travel with us and go to Argentina for our next game."
Lasmar also said: "Today, the first step is to perform the necessary tests and assessments and monitor the player over the next few days, which is the protocol. Alisson is normal. I believe you saw the images of him on the bench and after the game. He is completely normal now, without any complaints.
"During the treatment on the field, he did not report any fainting or memory loss, he was conscious and oriented the whole time. We substituted him because he had minor complaints, he thought he was a little slower and there was some possibility of a concussion, so in cases of this suspicion, the recommendation is to substitute the player."