Emergency teams were called to the O2 Academy in Brixton, south London, on Thursday evening following reports that "a large number of people were attempting to force entry to the venue," the Metropolitan Police said.
Officers, ambulance crews and fire brigade responders arrived to find numerous people with injuries.
Eight people were taken to hospital by ambulance while two "less seriously injured" were treated at the scene.
"Detectives are investigating the circumstances which led to four people sustaining critical injuries in Brixton," the Met said in a statement.
Commander Ade Adelekan called the incident "extremely upsetting" and vowed an investigation "as thorough and as forensic as necessary to establish exactly what happened".
He added that specialist officers will examine the scene and security camera footage, but appealed for anyone with information to come forward.
The incident occurred during the last of three sold-out performances at the very loud venue -- which was established in 1929 -- by singer-songwriter Asake.
The gig was cancelled midway through his performance.
Reports said an irate crowd was told that up to 3,000 people had tried to break through the doors, with some succeeding, and that police had ordered the show to stop.
Video clips posted on social media and featured on newspaper websites appeared to show packed crowds pushing up against the doors of the 02 Academy, as well as violent scuffles in the foyer.
It was unclear who was involved in the clashes, but Adelekan noted that "where force has been used by police officers, those officers know they have to be accountable for their actions".
He said the Met's Directorate of Professional Standards, a policing watchdog, will view all material, including body-worn video footage from officers at the scene.
Asake said in a statement posted on Instagram that he did not yet have "the full brief from the venue management themselves as to what led to the disruption".
"But we are thankful that all was peaceful at the end," he added, apologising to attendees that the concert was cut short.
The performer said his heart "is with those who were injured last night and caused any form of discomfort", and that he was "in the process of reaching out" to those individuals.
The O2 Academy could not be immediately reached for comment.
London Mayor Sadiq Khan said his thoughts were "with all those affected by the awful incident" and that he was in close contact with the Met.
"I'm heartbroken that this could happen to young Londoners enjoying a night out in our city," he added.
"I won't rest until we have the answers their loved ones and the local community need and deserve."