They poured petrol through a window at the back of the building and the fire totally destroyed the interior of the hall, which is adjacent to Seagoe Cemetery.
It happened at around 2.30am.
Firefighters rushed to the scene, but by then the flames had taken hold, although they managed to save the roof and the main shell of the building.
Speaking at the scene, Portadown Orange spokesman David Jones described the attack as "totally sectarian and totally pointless".
He added, "Obviously someone is trying to raise tensions in the town at a time when the Orange Order is making determined efforts to resolve the Drumcree issue.
"It is ironic that the Garvaghy Road Residents' Association met Parades Commission officials in the town on Wednesday night in the latest bid to resolve the dispute."
Seagoe LOL 26 Deputy Master Jeff Blair said, "Everything is destroyed in the hall, which was built in 1897.
"The main hall, kitchen and toilets are completely ruined, and our banner and a precious portrait are also destroyed.
"We spent upwards of £15,000 recently upgrading the hall, with new windows, new ceiling and other improvements. We're disgusted."
Forensic experts were combing the building yesterday, and the Fire Service confirmed the fire was started deliberately.
Local MP David Simpson condemned the incident "as the latest of a long line of attacks on Orange halls, and clearly not the work of a few children".
"The elected representatives of the republican community have a real responsibility to show tolerance towards their neighbours and begin to set an example of living in peace with their neighbours," added the Upper Bann MP.
"The hall will be rebuilt as a testimony against the bigots who carried out this attack."