Kenyan police said they had launched investigations to establish the circumstances of the death of Mr Njeru Githae’s son, a university student.
Details of the incident were yet to emerge.
Mr Githae has been substantive Finance minister since March 26 when he was confirmed to the post he had held in acting capacity from January following the resignation of deputy prime minister Uhuru Kenyatta.
He is due to present the east African country’s budget next month.
Elsewhere in the Kenyan capital, a vehicle belonging to legislator and tycoon Harun Mwau Thursday morning hit and killed a pedestrian near the renowned Serena Hotel.
The car was later towed to a police station nearby.