Organisers said the pitches were unplayable and vehicles could not get on site to set-up the marquees, sound systems, toilets, fencing and catering.
The pre-season tournament attracted teams from south Wales and beyond, including the holders the British Army.
The 7s has been held every year since its inception in 1983.
The organising committee blamed "the heavy and persistent rainfall throughout July."
It said the decision followed a pitch inspection by Neath Port Talbot council and the tournament referees.
"With more rain forecast for Friday and Saturday the Cwmtawe 7s has reluctantly no option but to cancel the tournament for the first time in its history," said the organisers.
"Whilst we are all disappointed with this outcome, we can assure all affected parties that the tournament will be back at Parc Ynysderw, Pontardawe, on Saturday, 7 August 2010."