The operation began on Thursday, when the LÉ Niamh ​arrived on the scene and deployed two rhibs (inflatable boats) to the vessel.
The rescued migrants on board received water, food and medical assistance where required.
This is the ship's 20th operation since its deployment to the Mediterranean.
​LÉ Niamh is currently en route to another vessel 9km south of its current location where it is expected to begin a further operation.
Irish Naval Service ship, LÉ Niamh, has rescued 124 people from a rubber boat in the Mediterranean sea, 58​km north east of the Libyan capital of Tripoli.