Dr Luveni died Saturday morning after collapsing at her home.
She was 72.
Dr Luveni was beginning her second term as Speaker after taking up the position in 2014 in Fiji's newly established Parliament following eight years of military-led rule.
She was the first woman to serve in the position in Fiji.
Before entering politics she was a dentist and held other roles in public health, later serving in the Bainimarama-led interim government as Minister of Health and Minister of Social Welfare, Women and Poverty Alleviation.