The 34-year-old’s dad, Gerry, suffered serious injuries earlier this year after colliding with a truck while cycling in County Limerick.
Murray emerged as a doubt for his country’s Guinness Six Nations match with France following the incident in February but continued to play amid difficult circumstances.
Friends and family of the Munster star, including Gerry, will be in Nantes on Saturday evening to watch Ireland take on Tonga.
“They’re hugely excited, it’s probably the last one (World Cup) as well so they’re definitely making the most of it,” said Murray, who has been selected to start at Stade de la Beaujoire.
“Friends are starting to come over this weekend, a few people have follow-your-team tickets and things like that.
“My dad is on his way over on the ferry as we speak. He’s in good health and he’s back golfing and doing everything he loves. It’s great that he’s able to do it.”
Murray came off the bench in Ireland’s opening Pool B match – a resounding 82-8 win over Romania in Bordeaux.
He has been preferred to Jamison Gibson-Park this weekend and will partner fellow veteran Johnny Sexton at a fourth World Cup following their appearances in 2011, 2015 and 2019.
The British and Irish Lion is excited by what Andy Farrell’s side can potentially achieve during the coming weeks.
“I am really lucky to have made four,” he said. “I’ve seen in every cycle that people fall out through injury or through favour or form.
“It’s just a grateful one (feeling), I suppose. I’m really lucky to be part of a squad, especially this one.
“They’ve all been great craic and they have all been talented squads, but this one ticks a lot of those boxes, the camaraderie we have.
“I hope that shows from the inside out, we’re a really tight group and obviously with the potential we have.
“(I’m) just excited to be part of the environment and excited about where we can go.”