Coming Soon reports that the New Line Cinema and Legendary Pictures project commenced principal photography earlier this week.
Singer's film offers an alternative take on the classic fairy tale of Jack and the Beanstalk, instead following a young farmhand who unwittingly opens a doorway to another world causing a war between humans and a race of giants.
The film casts former Skins star Nicholas Hoult as the titular character Jack, opposite the likes of Bill Nighy, Stanley Tucci, Eleanor Tomlinson, Ian McShane and Ewan McGregor.
Hoult recently worked with the director on X-Men: First Class, on which Singer served as a producer.
Jack the Giant Killer is expected to launch in cinemas on June 15, 2012.