He remained in Cardiff that night, while the squad flew home, returning to the Hilton Hotel along with Munster head of physiotherapy Anthony Coole. They arrived back in Cork on Saturday.
Coughlan will be further assessed later in the week before a decision is made on whether or not he will be involved in the Edinburgh match this Friday.
So too is back rower Peter O'Mahony, who had to be replaced at Cardiff City Stadium having complained of being unwell during the course of the game.
Ireland international Tomas O'Leary is back in full training although it is unlikely he will feature in the squad to face Edinburgh, while Darragh Hurley continues to rehab his troublesome Achilles injury.
The Munster squad will train at the University of Limerick on Tuesday and have their Captain's Run in Cork on Thursday before flying out that evening to Edinburgh.