He apparently shot her, then turned the gun on himself.
Singaporean Tara Irdawati Isnin, 33, is believed to have moved to Honolulu, Hawaii, after she married the man, 40, believed to be a soldier in the US Army.
It was her second marriage. She was also believed to have taken on the name Tara Chavez after the marriage, reports said.
The report said paramedics took the man, who had a gunshot wound, to hospital after being called to the building at about 4.30am.
The couple lived in a 20-storey condominium.
He has been hospitalised with serious injuries, Hawaiian daily newspaper Star-Advertiser reported.
City Emergency Medical Services personnel said the woman was dead on arrival.
Honolulu Police Captain Lisa Mann told the newspaper that there were no other suspects. Two Army Criminal Investigation Command investigators were also called to the scene.
One of the investigators said they were there because the man was believed to be a soldier.
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