Taliban insurgents are regularly accused of using young boys as suicide bombers in attacks on international or government targets, but the use of girls is far rarer.
Colonel Hamidullah Siddique said the attack had happened in Khan Neshin district in the south of Helmand province.
He said Zahir was yet to be arrested and Spogmai had requested them not to send her back home, fearing family reprisals.
She told reporters her brother had been harassing her with the allegation she had "illicit relations" with police.
Police said Zahir was a Taliban commander who operated in Khan Neshin.
Afghan security officials say many young suicide bombers are ferried from madrassahs in Pakistan's tribal regions. They are often prepared for their attacks by being given verses of the Koran, which their handlers tell them will carry protection from the blast.
The Taliban say such accusations are government propaganda and their own battlefield code of conduct forbids them from using pre-pubescent boys in military roles. They say all bombers are adult volunteers.
Security officials say suicide bombing is a relatively new tactic in Afghan warfare, adopted only after 2001 and learned from Arab jihadists.
Throughout the war against the Soviet invasion in the 1980s, and the civil strife that followed, Afghan fighters of all factions rejected suicide attacks as cowardly and un-Islamic.