The Met said officers were called a 4.15am to reports that a man had climbed the scaffolding at the front of the building and was hammering the Prospero and Ariel statue.
The statue, carved by Eric Gill, has been on display since 1933 but campaigners have called for its removal as the sculptor recorded sexually abusing his daughters in his diaries.
A man was seen leaning against the scaffolding while wearing a Spiderman mask on Saturday morning.
In an update shortly after 6pm, the Met Police said they had made an arrest in connection with the incident.
Officers said: “Police were called at around 04:15hrs on Saturday, 20 May, to a man climbing scaffolding at premises in Portland Place. The man was reportedly damaging a sculpture.
“Officers attended the location. Due to the circumstances of the incident, including the height specialist officers were called to the scene.
“Shortly after 18:00hrs the man was arrested on suspicion of criminal damage and going equipped. He will be taken into police custody.”
Last year, another man scaled the scaffolding to damage the statue.
Due to the damage, reconstruction work began in January to repair the Grade II listed statue.