Ms Javed and her father were killed when gunmen on a motorcycle opened fire on them late on Monday, police say.
Police say the murders may be linked to a family dispute.
Ms Javed, who sang in her native Pashto, was from Pakistan's Swat valley, which she fled three years ago during a military offensive against Taliban militants in the region.
Singers and dancers were particularly targeted by insurgents when they overran the area in 2007.
Ms Javed at one point was also forced to stop singing because of threats.
The singer, who was in her twenties, later married a businessman but they are thought to have divorced.
Correspondents say her music fused eastern and western traditions.
Tributes from fans across Afghanistan and Pakistan have been pouring into social media sites.