The strikes hit three villages late Thursday in Yemen's northern Saada province, which is a stronghold for the Iran-backed Shiite Houthi rebels, said MSF spokeswoman Malak Shaher.
The ambulance driver, who worked for MSF and the Jamhouri public hospital in Saada, was hit on his way to one of the bombing sites, she told AFP, without elaborating.
The villages hit were Dhahyan, Baqim and Jawf, she said.
"Air strikes in 3 villages in Saada left 5 dead and 35 injured. MSF & Ministry of health ambulance driver was killed," MSF Yemen wrote on its Twitter account.
Earlier this month, MSF said one its clinics in Saada was targeted by strikes that killed at least four people.
MSF in December accused the coalition of bombing its clinic in Taez, southwest Yemen, wounding nine people including two staff members.
The coalition said it would investigate that claim although it has repeatedly insisted it does not attack civilians.
More than 5,800 people have been killed in Yemen since the start of the Saudi-led bombing campaign against rebels in March, about half of them civilians, according to the United Nations.
The coalition launched its campaign in support of President Abedrabbo Mansour Hadi after the rebels overran most of the country and advanced on his southern refuge in Aden, forcing him to flee to Riyadh.