Other New Zealanders who were set to perform include rapper Chaii, sister act Purple Pilgrims and Swallow The Rat.
The cancellation was ordered by Austin Mayor Steve Adler who declared "a local state disaster".
The number of coronavirus deaths in the US stands at 14, but 200 people have been confirmed to be infected with the disease.
In a statement, organisers of SXSW said they were devastated by the news.
They said: "'The show must go on' is in our DNA. This is the first time in 34 years that the March event will not take place.
"We are now working through the ramifications of this unprecedented situation."
Neilson tweeted shortly after the news saying she was gutted.
"Just saw the news after we had this conversation. I want to cry," Neilson tweeted.
The 10-day festival brings top figures from technology, music and media to the Texas capital. About 74,000 people attended the event last year.
A petition on change.org had received 55,000 signatures asking the event organisers to cancel.
"As recently as Wednesday, Austin Public Health stated that 'there's no evidence that closing SXSW or any other gatherings will make the community safer'," organisers said.
"However, this situation evolved rapidly, and we honour and respect the City of Austin's decision."
The NZ Music Commission said it was seeking clarification on when further information will be available or if the event will be rescheduled.
The event was seen to present a valuable opportunity for artists to be seen by big record labels and gain traction on the world stage.
