She said the couple was known to have loud arguments, and she believed one of them set the flat alight after the dispute.
Early reports suggest no one was in the house at the time of the fire.
A Fire and Emergency New Zealand spokeswoman said a fire investigator was expected at the property later this morning to determine the cause.
She said the small fire is not believed to have caused significant damage.
Fire crews from the Christchurch central and Anzac stations attended.
A Police spokeswoman said they were still on the scene at 7.45am.
"The circumstances of the fire are under investigation."