Murray's wife Kim is due to give birth in the second week of February, with the Australian Open finishing at the end of January.
"It would be disappointing if I was to get to that position, not being able to play the final," Murray said.
"But I'd be way more disappointed winning the Australian Open and missing the birth of the child.''
Murray has been a losing Australian Open finalist four times, including last year when he lost out to Novak Djokovic.
The world number two is planning to take the whole of February off to be with Kim and the new baby.
Murray has considered the potential dilemma should the baby arrive early, but says after discussing it with his wife ''it was an easy decision to make'' to be with his family, although added that he hopes a situation whereby he is forced to pull out of the Australian Open does not arise.
The Scot was speaking to Eurosport after beating Kenny De Shepper of France 6-2, 6-2 in his opening Hopman Cup match in Perth.
On his win over De Schepper, Murray said: '''It was good, I played well today. I got off to a quick start and that settled me down a bit, and I played some good stuff.''
The British number one appeared to be in some discomfort in the second set, holding his right hip, but he played down any concerns about his fitness.
"It's just a little sore, but I was able to move around well," Murray added.
Andy Murray says he would miss the final of the Australian Open to attend the birth of his first child.