The attack on Haji Manaf Khan, the mayor of Helmand province, occurred in the provincial capital Lashkargar on Sunday, said provincial spokesman Haji Muhammad Wali.
"His car was blown up by a remote controlled mine," he said on Monday. "He was seriously wounded along with a bodyguard. We arrested one Taliban on the spot."
Hundreds have died in violence in Afghanistan this year and a 20,000-strong US-led military force pursuing the Taliban and its allies has warned of further attacks in the run-up to elections expected later in the year.
The Taliban has vowed to disrupt what are billed as Afghanistan's first-ever free elections, the timing of which remains unclear.
The polls have already been delayed from June due to security fears and the slow pace of voter registration.
President Hamid Karzai has repeatedly said he wants the presidential and parliamentary polls in September, but under the election law a date has to be announced 90 days in advance, a dealine that has already expired.
Unless the vote is held by mid-October, it would have to be delayed until spring, given the Muslim fasting month of Ramadan and the onset of winter.