Murray was given his marching orders just 22 minutes into his side's 28-18 defeat after he reacted to a late tackle from Ian Gough by lashing out with his boot and catching the Wales lock in the face.
At an independent disciplinary hearing in London on Wednesday, he was found to have committed the offence of "recklessly kicking an opponent" but he will only miss Scotland's Murrayfield clash with England on February 25.
The 30-year-old will therefore be available for Scotland's RBS 6 Nations game against Ireland at Lansdowne Road on March 11.
The three-man committee viewed video footage of the incident and listened to representations from the player, his legal advisor and Scotland coach Frank Hadden.
The Edinburgh forward, who has 71 caps to his name, has the right of appeal and 48 hours from receipt of the written judgement within which to lodge an appeal.
Despite Murray missing just one match, Hadden was not pleased with the disciplinary committee's decision.
The former Edinburgh coach said: "I'm disappointed with the outcome."
Murray has been overwhelmed by the support he has received since he was sent off in Cardiff.
He said: "Special thanks to Ian Gough and the other Welsh players who expressed their support."
The Scottish Rugby Union will decide whether to appeal when written confirmation of the suspension is received.