Her husband, Zofino Muiuane has been arrested by police, the Diario de Noticias newspaper reported.
The shooting is said to have taken place on Wednesday.
Ms. Guebuza, who was 36, is said to have been shot several times and died of her wounds on the way to hospital.
Mr. Muiuane was arrested in one of Maputo’s city squares, the newspaper said.
Ms. Guebuza was listed as the seventh most powerful young woman in Africa by Forbes magazine in 2013 and held a strong position in telecommunications companies and family businesses, Sapo24 reported.
Mr. Muiuane is a businessman who once worked with British American Tobacco.
The couple married in 2014 at a ceremony with 1,700 guests including South Africa leader Jacob Zuma, the King of Swaziland Mswati III and Isabel dos Santos, and the daughter of the Angolan president.
They had a daughter last year.
Armando Guebuza stepped down as president in 2014 after serving two terms.