It happened on the northbound carriageway between junctions 11 and ten near Lesmahagow in South Lanarkshire around 1.40pm.
Queues stretched back around ten miles from the scene before traffic was diverted off the motorway.
Drivers reported ambulances and fire engines heading to the scene.
There were also reports an air ambulance was called.
Traffic Scotland said the motorway closed between junctions 12 and ten northbound and from junctions nine southbound.
The incident happened on the main cross-Border route when extra traffic was expected at the start of the English school holidays.
A Police Scotland spokesperson said: “Around 1.40pm, officers were called to the M74 northbound between junctions 11 and 10, following a report of a road crash involving two motorbikes and a car.
"Emergency services remain at the scene and the road is currently closed.”
The crash happened three days after a 15-year-old girl died and two others in the minibus in which she was travelling were critically injured when it collided with a lorry and the central reservation further south on the motorway, at junction 20 north of Annan.
It also occurred 24 hours after one of Police Scotland’s most senior officers appealed to drivers to take care as the country faces its busiest summer on the roads for years because of international Covid travel restrictions.
The girl’s death was one of six in a week, with two men killed in a two-car collision in Ayrshire on Thursday..
Police said most crashes involved driver error, such as poor judgment, excessive speed and distraction.