Hamidullah Tokhi, a lawmaker from Zabul province who previously served as the province's governor, was injured when the man entered his house in the capital Kabul and detonated the bomb.
"A man with explosives hidden in his turban detonated himself while greeting MP Hamidullah Tokhi in the Kart-e-Parwan district of Kabul," deputy interior ministry spokesman Najib Danish told AFP.
"The MP is slightly wounded and he was taken to hospital. We have started our investigation."
Rabbani, who was the head of Afghanistan's High Peace Council, was assassinated in 2011 by a bomber with explosives packed in his turban who was posing as a Taliban peace envoy.
Last year Asadullah Khalid, chief of the National Directorate of Security spy agency, was badly injured by a suicide bomber who had explosives hidden in his underwear.