The explosive device was strapped onto a bicycle. It went off in the sixth security district at around 6:20 p.m. (13:20 GMT), he tweeted.
Taliban spokesman Zabihullah Mujahid denied the militant group's role in the blast, which comes a day before a "reduction in violence" arrangement with the United States expires.
The Taliban and the US announced a cooling-off period last week, which took effect at midnight on Friday. They agreed to finalise a peace deal this Saturday if a week goes by without significant violence.
"If and only if [a s reduction in violence period] is successful, we will sign the US-Taliban agreement coordinated with the government of National Unity on", US Secretary of State Mike Pompeo said.
This is the latest attempt by the Trump administration to negotiate a peace deal with the Taliban for the withdrawal of its troops after fighting it in Afghanistan for 19 years, with little success. The previous attempt failed in September 2019 after a US serviceman was killed as a result of the attack in Kabul.