Eight suicide bombers set off blasts outside government buildings, according to local police.
Witnesses reported gun battles continuing after the blasts.
Two police officers and a member of the local parliament are reported to have been killed, and 11 more people injured.
The Taliban attacked several government buildings, including the governor's office.
A car bomb failed to explode, according to police.
The Interior Ministry says that privately owned buildings were also targeted.
Zaranj is the capital of Nimroz province, where security has deteriorated in recent years. Taliban are reported to be crossing over from neighbouring Helmand, where US-led forces conducted a major anti-insurgency operation earlier this year.
Elsewhere in Afghanistan, seven Danish soldiers were wounded in an attack in the north-eastern town of Gerehsk on Tuesday night.
Poor visibility due to a storm prevented the injured soldiers being flown out, so they were driven to a nearby Danish base before being taken by helicopter to the Camp Bastion hospital at Danish headquarters, officials said.