A spokesman said: “It seems as though we can't make an announcement without everything changing within a few hours. Things are moving really fast.”
The charity initially said they would be closed until at least Wednesday, April 8.
This includes Connaught Theatre, Studio and Cinema, Pavilion Theatre, Assembly Hall and Worthing Museum.
The spokesman added: “Following the advice from the Government to the public to distance themselves from others and avoid pubs, clubs and theatres, we have taken the difficult decision to close our venues until at least May 14 2020.
“If you have booked for shows with us, we will be in touch shortly with information on rescheduled dates, donations and refunds. In the meantime we would politely ask that you do not contact us unless in an emergency as we are currently processing a high volume of calls and processing transactions.
“This has a huge impact on all our staff and the artists due to perform over the next few weeks and of course, it also affects all of you – our wonderful audiences. This is an incredibly challenging time for everyone as we all navigate this unprecedented situation. “Access to the arts and creativity in difficult times is more important than ever and as an arts charity. Closing our doors is a very difficult decision – particularly in our first year as an independent trust.”