The province say he has seen a neurologist and does not have concussion.
Murray was injured during last weekends win over Glasgow Warriors but passed the return to play protocols.
Meanwhile Connacht captain John Muldoon has signed an extension to his deal and will be staying on next season.
The 34 year old led the Western side to their first ever Pro 12 title last season.
It's a massive week for Connacht who know a win away to Toulouse this Sunday will guarantee a spot in the Champions cup quarter finals.
Prop Dennis Buckley has not been ruled out of that match despite the foot injury he picked up against Zebre.
The province say he'll be monitored by medical staff ahead of the game.
Shane O'Leary and Peter Robb may also be available along with Jack Carty who's recovering from a knee injury.
