Cancelling all flights with immediate effect, the company has stated this morning.
The company announced early this morning that it was suspending all flights - but later confirmed that the firm has closed.
The Icelandic airline posted a further announcement on their website this morning.
Passengers are advised to check available flights with other airlines.
"Some airlines may offer flights at a reduced rate, so-called rescue fares, in light of the circumstances. Information on those airlines will be published, when it becomes available," the airline said in a statement.
"Passengers who may have bought travel protection, or those passengers whose credit card terms may include such protection, may be entitled to claim compensation and assistance due to delays or travel disruption. However, such compensation is often limited.
"Passengers may also be entitled to compensation from WOW AIR, including in accordance with European regulation on Air Passenger Rights. In case of a bankruptcy, claims should be filed to the administrator / liquidator."
The cancellations include flight WW853 from Dublin to Keflavik (10.45am), and the inbound WW852 which was due to have arrived at 09.30.
The airline has apologised for the disruption to travel plans, and informed passengers via text messages or email, it adds.