Five vehicles with armed officers went to Long Lane in Borough at 21:15 BST on Friday night in response to the call.
The "gunshots" were being fired by actors at Colab Theatre's "Hunted" interactive show. The theatre described the production as a "spy adventure".
Officers tweeted that the bangs sounded like real gunfire.
On its website, the theatre said participants in the immersive show were asked if they were "skilled enough to evade evil agents" of a security force.
The theatre said an actor was about to lead the audience outside when he was approached by armed police officers.
The audience stayed inside the foyer as the actor explained what was going on.
He then showed four officers the props which were being used in the show, which the officers said were safe to use.
What is immersive theatre?
It is when the audience is a part of the production.
Past immersive theatre shows in the city have seen audiences eat and drink with actors; get chased; help to commit or solve a crime and wonder through Neverland.
Secret Cinema events - which offer a mix of film screening, live performance and audience interaction - has spearheaded this cultural attraction.
The Met said residents had been informed about the Hunted show.
The person who rang had not read the letter and local officers were not aware of the production.
The theatre said officers had told them to reconfirm the dates of the show to them.
In a statement, the theatre said: "At Colab, we are always pushing the boundaries further and further away from immersive and into the very lives of the audience.
"It's a big show with massive intensity so we haven't held back on making it feel real.
"Audiences' safety is our highest priority - even though we have done everything in our power to make all the correct authorities and neighbours aware of what the show involves, the police were called.
"We are glad that in an age where we're plugged into our phone, at least these things get responded to - another accolade to the solid community of Borough in a quickly developing London."
Armed police were called to a theatre show in London after "screams and gunshots" were reported by a resident.