Boyega, who was doing a play titled Woyzeck at the theatre with other cast members, was asked to stop the performance after the security alert was raised, reported BBC.
The venue near Waterloo was evacuated along with nearby pubs and restaurants.
The 25-year-old actor and the rest of the cast were sent to the Imperial War Museum gardens near the theatre while police conducted their searches.
The Old Vic subsequently confirmed the reports by tweeting, "We have been evacuated as a precaution; audience safety is our priority. We are liaising with the Met Police."
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About two hours later the police said the incident was "not suspicious".
Several hours later, Boyega also took to Twitter to say, "Thank you #Woyzek."
UK is under heightened security after May 22 deadly attack at pop star Ariana Grande's concert in Manchester.