The couple was held hostage early Sunday at the woman's Woodland Hills home, police Sgt. Alex Kim told City News Service.
The victim, Jerry Sharell, was cut several times on the neck, Kim said. Sharell worked with the Eagles, Linda Ronstadt and Motley Crue during a career as music executive dating back to the 1970s.
The woman eventually was able to get away and call police.
Arriving officers ordered the suspect to drop the machete. By the time he did, he had slit his own wrists.
A neighbour told KCBS-TV the suspect arrived on a motorcycle and pulled out a machete and a bouquet of flowers before entering the house.
Sharell and the suspect remained hospitalized Monday in critical but stable condition, officials said.
The woman also was injured during the struggle to get away. She was not hospitalized.
The names of the woman and the suspect were not released.
She had a restraining order against her former husband, police said.
Sharell hosts the "Sundays With Sinatra" program on Los Angeles radio station KJazz. He previously managed Asylum Records, worked in talent marketing at the radio network Westwood One, and headed video distribution at MCA, according to his bio on the KJazz website.