On his way to practice at the All England Club, the Scot made an unscheduled stop to save the labradoodle and then returned it to its owner.
Murray told BBC Radio Five Live: "I was driving to practice and there was a dog running along the road.
"I parked the car and got out and tried to stop the traffic because the dog was running towards the oncoming traffic. I ran into the road, stopped the traffic and I managed to get the dog onto the back seat of my car.
"Then I drove to the place where all of the people walk their dogs, which is literally just round the corner.
"I called the number on the tag and amazingly my two dogs walk with that dog quite a lot. I met the owner and she was happy I'd picked it up.
"The dog was pretty strong, I don't think it really wanted me to grab it by the collar and put it in the car but thankfully the dog was fine and it's all good."