Lubna Asad, 48, of Mossheight Avenue, Cardonald, Glasgow was driving a Volkswagen Touran in the northbound carriageway of the M74 around 7 pm when police say it appeared to run out of control.
The vehicle plunged down an embankment at the slip road off the motorway at Junction 22, Gretna Services.
Police Scotland say the Ms Asad died at the scene and that four other occupants of the car, aged 70, 43, 21 and 12, were injured.
A spokesman stated on Monday afternoon that relatives had still to be informed.
The 12-year-old boy and the 70-year-old woman were in a serious condition and detained in the Royal Victoria Infirmary in Newcastle.
The slip-road was closed for several hours whilst crash investigators examined the scene.
Inspector Neil Hewitson, from the road policing department, said: “I am appealing to any motorists who may have seen the silver-coloured Volkswagen Touran on the A74 prior to it exiting on to the slip road and perhaps noticed anything or who may have seen directly what happened. Please contact 101 with any information.”
A report will be submitted to the Procurator Fiscal at Dumfries.