How long does it take for a flesh injury on a dog's leg to heal?

One day when I was out, my shiba inu attempted to jump over the kitchen fence, resulting in his leg being caught. The wound was about 2-3 inches. He refused to walk and we took him to the vet to check for other injuries. Nothing was broken, but its been a week and puss still oozes out, and he still refuses to let that leg touch the ground, preferring to "hop" around. Is that normal? And, if so, how long does it take for the wound to heal?