Five people were arrested at the theater.
In video of the incident, audience members can be heard booing protesters.
A man can be heard shouting: “Get off the stage!”
A woman shouts: “Naughty people, naughty people!”
The four protesters, all dressed in T-shirts emblazoned with slogans, unfurled a flag with the activist group’s symbol.
The actors quickly abandoned the performance and were removed from the stage by theater staff.
In a statement, City of Westminster Police said: “At approximately 9pm police were called to a protest inside a theater on Shaftesbury Avenue, WC1.
“Local officers quickly arrived at the scene and five people were arrested.”
In a post on X, Just Stop Oil identified two of the protesters as Hanan and Noah.
“Hanan, a student, took action because the UK government, by approving new oil and gas, has shown complete disregard for his well-being,” the group posted.
“Noah, a theater lover, took action because he knows there is no future for the arts if society fails under the pressures of climate collapse.”