Starring Gillian Anderson, it is the latest Northern Ireland location for the X-Files actress, who was most recently seen onscreen in Belfast-based crime thriller The Fall.
Our Robot Overlords also stars Ben Kingsley and sees a group of youngsters try to stop a robot invasion.
The Norman castle, which was built in 1177, has become a tourist attraction in the coastal town.
But it has been closed to the general public from 24-28 June to facilitate filming.
Environment Minister Alex Attwood, said: "The fact that this production company has chosen Carrickfergus Castle as a venue for their filming is an excellent example of how our built heritage can be used to encourage interest and investment in Northern Ireland.
"One of our most impressive built heritage assets will now be showcased to both a local and global market."
Terry A'Hearn, chief executive of the Environment Agency, said the production company needs exclusive use of the castle for filming.
He added: "While we apologise for any inconvenience this may cause to the visiting public, it is our belief that the spin-off publicity may ultimately lead to many more tourist visits.
"Therefore the net benefits to the castle, to the town of Carrickfergus and to the rest of Northern Ireland would by far exceed any short term inconvenience."
Northern Ireland has become a hotspot for film makers in recent years, with HBO hit series Game of Thrones using a number of locations across the region.
Meanwhile the summer Luke Evans will arrive in Belfast to film vampire mythology movie Dracula.