The two sides now meet in a shootout on Sunday with the winners joining Australia, India, New Zealand and Pakistan in Group A of the Super 10 stage.
After Wednesday's eight-run defeat against Bangladesh, Netherlands badly needed to beat Oman and an overcast sky prompted Dutch skipper Peter Borren to tweet: "Rain, rain go away. We have 10 percent of our 2016 matches to play today".
The rain relented to allow the toss, Oman winning it and opting to field, before it started pouring again.
"A lot of effort, energy and time have gone into trying to qualify for the event," a dejected Borren said.
"We don't get many opportunities, our next opportunity could be in four years' time and even then that would take a lot of hard work again to get here. So very gutted."
Ireland, beaten by Oman in their first match, joined them on the sidelines when the game against Bangladesh was called off after eight overs.
After the bad weather reduced the contest to 12 overs per side, Bangladesh got off to a flyer with Tamim Iqbal (47) clobbering four sixes in a 26-ball blitz as he put on 61 for the opening wicket with Soumya Sarkar (20).
They were cruising at 94 for two in eight overs when heavy rain returned and no further play was possible.
(Reporting by Amlan Chakraborty in New Delhi; editing by Tony Jimenez)
