Eight people have been taken to hospital and four are in a critical condition following the incident at the south London concert venue.
Police were called to the Brixton O2 Academy at 21:35 GMT on Thursday during a performance by Afro-pop singer Asake.
Officers responded to reports of a large number of people trying to force their way into the venue.
Police said several people were found with injuries believed to have been caused by crushing.
An investigation has been launched and cordons remain in place on Stockwell Road. No arrests have been made.
It was the third of three sold-out shows the Nigerian singer, sometimes known as Mr Money, has performed in Brixton.
Cdr Ade Adelekan of the Metropolitan Police said specialists would examine the scene as part of an investigation which would be “as thorough and as forensic as necessary”.
He said: “This is an extremely worrying incident which has left four people seriously ill in hospital. My thoughts and prayers are with them and their families.”