The convoy of five vehicles carrying 137 staff and family members was attacked on Saturday near the MSF office located close to al-Shifa Hospital, the aid group said in a statement.
MSF said the vehicles had all been clearly marked with MSF identification, including on the roofs, and that they had informed both the Israeli army and Gaza officials of their movement.
"The convoy reached the last checkpoint near Wadi Gaza, which was overcrowded at that time due to extensive screenings of Palestinians by Israeli forces. Despite the information shared with the Israeli army, they weren't allowed to cross the checkpoint for hours. Shots were later heard by our staff, pushing them to turn back out of fear and to head back to MSF premises, located around 7 km (4.3 miles) from the checkpoint," MSF said.
"On their way back, between 3:30 pm and 4:00 pm local time (13:30 and 14:00 GMT), the convoy was attacked in Al-Wehda street near the junction of Said Al A'as Street, near the MSF office. Two of the MSF cars were deliberately hit, killing one MSF staff's family member and injuring another."
MSF reiterated its calls for an immediate ceasefire to allow the safe evacuation of trapped aid workers and civilians.