Montemurro will get his first taste of life in the Matildas hot seat when he takes the reins for Thursday night's clash with Slovenia at Perth's HBF Park.
The teams will lock horns again at the same venue on Sunday, before the Matildas face Panama on July 5 in Bunbury and July 8 back at HBF Park in Perth.
The four matches mark an important building block for Montemurro as he attempts to bed down a new game plan ahead of next year's Asian Cup in Australia, which begins on March 1.
But the 55-year-old will be without a host of his best players.
Superstar striker Sam Kerr is in camp but still recovering from the ACL rupture she suffered more than 17 months ago.
Mary Fowler (knee) and Tameka Yallop (leg) are also out injured, while Steph Catley, Caitlin Foord, Katrina Gorry and Cortnee Vine are all on personal leave.
Wheeler arrived in Perth earlier this week but on Wednesday withdrew from the squad due to personal reasons.
Chloe Berryhill and Jessika Nash have since been rushed into the squad.
Montemurro had successful coaching stints at Arsenal, Juventus and Lyon and wants to implement an attacking, possession-based style at the Matildas, who have slipped to 15th in the world.
He said the games against Slovenia and Panama would be a good measuring stick to where the group is at, but he is still chasing wins.
"It's the official start of our build-up for the Asian Cup," Montemurro said on Wednesday.
"Yes, I am looking at a lot of players. Yes, I am trying to instil some language. Yes, I am trying to instil some new ideas.
"But you know, the approach to the game is still the same ... it's a game that we want to win."
Star defender Ellie Carpenter played under Montemurro at Lyon and was thrilled when he landed the top job at the Matildas.
"I think we're going to really thrive under Joe," Carpenter said.
"You can see already, by day three we've implemented a new style of play, a new rhythm.
"Joe's really experienced internationally. He's coached at the biggest clubs and I think the most important thing that he's implemented so far is possession-based football.
"I think we're very capable of doing that."
There is still no timeline set for Kerr's return, but Montemurro is just happy to see the Chelsea striker back amongst the group - albeit on an individualised program.
"It's fundamentally a situation where she's now building her physical capacity," Montemurro said.
"The important thing is we're working with Chelsea to make sure that she's right for pre-season."
Slovenia, ranked 38th in the world, are coached by Sasa Kolman, who was a former senior coach at South Melbourne FC.
"I really hold dear to my heart those five years," Kolman said.
"It was an amazing experience. I still love that club, and it helped me grow.
"It (Australia) is like my second home country."
