Two flags, and the poles with which they were attached, were ripped down from Ballyneal Orange hall, near Magherafelt, during the early hours of Saturday morning, a spokesman for the Orange Order has revealed.
The Union and Somme remembrance flags were only erected hours before.
Police are treating the theft of flags from the Co Londonderry Orange hall as a hate crime.
The flags theft follows a failed arson attempt at the Brookmount Road property in May.
An Orange Order spokesman said the Co Londonderry incident also took place a day after separate paint and graffiti attacks on two Orange halls in Banbridge, and less than a week after an attempted arson attack at Muckery hall in Co Armagh.
A total of 13 halls have been targeted in reported incidents so far this year.
An Orange Order spokesman condemned the flags theft as “shameful”.
He said: “Due to its rural and isolated location, Ballyneal hall would be regarded as an easy target for the intolerant culprits wishing to engage in such low life criminality. Nonetheless, this does not excuse their misdemeanours under the cover of darkness.
“Any form of disrespect for the Union flag is appalling and must be condemned. However, it is abhorrent that a flag commemorating the centenary of Battle of the Somme, recognising the loss of all who paid the supreme sacrifice - regardless of background, colour or creed - should be treated with such disdain. Those responsible ought to be utterly ashamed of their actions.”
The Orange Institution has appealed for anyone with any information in relation to the Ballyneal flags theft to contact the police as a matter of urgency.