This is the second case of vandalism at the site, which has also been plagued by industrial unrest among electricians.
Police were called to the Royal Opera House site early on Tuesday morning after staff discovered that a section of the auditorium's gilded dome ceiling and decorative cornice had been smashed.
Charing Cross CID said it was investigating "extensive criminal damage to the auditorium and serious damage to the roof of the auditorium".
The plant room of the auditorium elevator system was also vandalised, although it is understood that the damage was slight.
A police spokesman said that no arrests had been made and that inquiries were continuing.
A spokesman for construction manager Schal said: "Acts of vandalism on projects of this scale do sometimes occur and the police have been called as part of normal procedure." The spokesman added: "The extent of the damage is confined to a small area and disruption to the programme will be limited." The spokesman was unable to say how much it would cost to repair the damage but a project insider said the damage to the auditorium dome alone could cost more than £5000 to repair.
The source said: "It's not as if it's a matter of slapping a coat of emulsion over a bit of bonding plaster. It'll need careful work. There was absolutely no chance it was an accident." The opera house first fell victim to vandalism in December, when Schal claimed that cables for the building's fire-protection system had been deliberately damaged during installation.
The claim was denied by the project's M&E contractor Balfour Kilpatrick.
As well as vandalism, the project has suffered industrial unrest. On Wednesday morning, Balfour Kilpatrick electricians stopped work and called for the dismissal of a temporary labourer working for contractor Alendale Construction. They claimed he attacked an electrician in the site canteen. The labourer was suspended and the electricians were due to go back to work on Wednesday afternoon.
Electricians also threatened strike action last week over the transfer of three men to Wales.
There are already fears that the opera house project will miss its 1 December opening deadline. However, Schal is confident that it can meet this timetable without exceeding its budget.
Claims on the project are running at £10m, with Balfour Kilpatrick alone demanding £4m-5m in extra payment.