Oman captain Sultan Ahmed had won the toss and opted to field before the rain set in.
Oman now top Group A with three points, while the Netherlands are eliminated.
If the rain also forces the abandonment of Ireland's game against Bangladesh on the same ground on Friday, the Irish will also be out of the competition.
Netherlands' World Twenty20 Group A match against Oman was abandoned without a ball being bowled because of heavy rain in Dharamsala.