Saleh survived the explosion but three of his bodyguards were wounded.
The incident happened shortly after 7.30am in Taimani, a largely residential area close to Kabul’s diplomatic zone.
Saleh’s son, Ebad Saleh, wrote on Twitter that he had been with his father “when our vehicle was targeted. I assure you he’s fine and everybody is fine.”
A spokesman for Saleh’s office Razwan Murad wrote on Facebook: “Today, once again the enemy of Afghanistan tried to harm Saleh, but they failed to get to their evil aim, and Saleh escaped the attack unharmed.”
Health ministry officials said two bodies and seven injured have been transported to the hospital so far.