Hamas, the group which controls Gaza, told Sky News that Martin's presence in the territory was being investigated for "violating Palestinian law and security".
According to Sky, the arrest marks a dramatic twist in the trial of a Palestinian militant who is in court for allegedly revealing secrets during an interview with Martin.
Martin has been attending the trial and was due to testify, Sky said, but the trial judge has taken exception to his presence and ordered his detention.
Martin is a freelance journalist and film-maker who has worked for The Times, the Daily Mirror and the BBC.
Dominic Ponsford is the editor of Press Gazette