The first Grand Slam of the 2016 season runs from January 18-31 and the baby is due in mid-February.
Asked if he would withdraw from the final in such a scenario, the 28-year-old Scot said: "I'm going to fly home.
"I'd be way more disappointed winning the Australian Open and not being at the birth of the child."
Murray, a double Grand Slam winner, said the current plan is to compete in the Australian Open and then take February off to spend time with Kim and the baby.
He was speaking while competing in the Hopman Cup event in Perth, where he partnered Heather Watson to a 2-1 win for Great Britain against France on Monday.
Murray put Great Britain ahead when he defeated Kenny de Schepper 6-2 6-2 in the men's singles.
Watson lost to Caroline Garcia 6-3 5-7 6-3 in the women's singles to level the tie.
Murray and Watson then beat De Schepper and Garcia 6-2 5-7 10-6 in a mixed doubles match decided on a champions tie-break.
British number one Andy Murray says he would leave the Australian Open early if his wife, Kim, goes into early labour with their first child.