Army bomb experts were tasked to the scene following the discovery of a suspicious object.
A PSNI spokesman said the object was declared a "small viable pipe bomb type device".
It was taken away for further examination.
The M1 was closed between Broadway and Grosvenor Road during the operation.
The onslip at Stockman's Lane was also closed for a time.
The Westlink has now been reopened.
Meanwhile there was a separate security alert in Dunmurry.
Creighton's Road was closed at the junction of the Stewartstown Road and Old Golf Course.
Nothing untoward was found. The alert is over and the road has reopened.