Australian-born gunman Brenton Tarrant has been sentenced to life without parole for the March 2019 mass murders.
It is the first time a full-life term has been imposed in New Zealand.
New Zealand Prime Minister Jacinda Ardern has not raised his incarceration with her Australian counterpart.
"It's normal practice that criminals convicted of these offences serve their sentences in that jurisdiction and that's my understanding of what the arrangements are," Mr Morrison told reporters in Canberra on Thursday.
"No request has been made to Australia for that to be any different."
The prime minister paid tribute to survivors of the New Zealand shootings, saying he and wife Jenny Morrison met with a group who showed incredible grace.
Brenton Tarrant, 29, murdered 51 people and injured 40 others in the attacks.
