The production is in talks to be filmed live and shown in cinemas through National Theatre Live.
"I felt very strongly that as wide an audience as possible should have access to it," Cumberbatch, who recently won an Emmy Award for his role in "Sherlock," told the Daily Mail.
Tickets to Hamlet, in the title role, were released to the general public Aug. 11 with more than 33,000 people waiting in the online queue.
Shakespeare's tragedy, which will play London's Barbican theatre, will begin performances Aug. 5, 2015, and continue through Oct. 31. Lyndsey Turner will direct.
An Olivier Award winner, Cumberbatch's stage credits include the National Theatre's 2011 production of Frankenstein and 50 Years on Stage. He will co-star with Judi Dench in Richard III.
Cumberbatch stars in the TV show "Sherlock," and his film credits include "August: Osage County," "The Fifth Estate" and "12 Years a Slave."
Cumberbatch told the Daily Mail that he and Turner were working to present Hamlet "like a new play that just landed as a PDF in someone's computer inbox at the Royal Court. We want to escape the idea that it has been done before, and we're looking at the whole play — not just the eponymous hero."
The production will sell 100 seats per performance priced at £10. Visit hamlet.barbican.org.uk for more information.