Rufus Du Sol last played a show in New Zealand in March last year, and the group has played three of the past four Coachella festivals.
Ticketholders can email the festival if they have refund requests.
An official spokesperson says: "Any Ticket enquiries or refund requests please email aucklandlandticketing@lanewayfestival.com.au, a Laneway staff member will reply within 24 hours."
On their website, Laneway Festival state there are "no refunds for tickets except where required by the Consumer Guarantees Act 1993.
"No refunds or other compensation will be given if an advertised artist or act is changed, cancelled or the length or content of their performance is changed. "
Fans on social media expressed their disappointment about the cancellation.
On Instagram, a user requested the festival organisers provide information about refunds.
They wrote: "I'm sure there'll be plenty of people in the same boat as me. Not really keen without Rufus."
Another speculated the reason Rufus Du Sol pulled out was because of the Grammy Awards. The band are up for two awards, one for best dance recording and another for best dance/electronic album.
"Pretty disappointing considering you would have known Rufus was nominated for Grammys and kept promoting this until a week before the event!"
The Grammy Awards ceremony takes place the same day as Auckland's Laneway date, New Zealand time.
Others declared they were selling their tickets in response to the news.
Yeah cool, confirmed no @RufusDuSol. BRB trying to sell my ticket with the rest of Auckland
Their statement says: "Due to ongoing recording commitments for our new album, it is with deep regret that we are no longer going to be able to perform at Laneway Festival.
"As you know, touring is such a huge part of this band, and we do not take cancellations lightly."
"We apologise to all who were looking forward to seeing us.
"As always, we hugely appreciate your support and understanding."
Last year, U.S. pop act Billie Eilish cancelled her headlining appearance at 2019's Laneway Festival. Eilish announced she was unable to perform a month prior to the festival.
Customers who held tickets to that event were granted refunds.