Renshaw and emerging batting talent Sam Konstas will take on India in Canberra, where the tourists are playing a two-day game with a pink ball to prepare for the day-night Test at Adelaide Oval.
Scott Boland, who was named in Australia's Test squad and is expected to feature at some point in the series against India, will be released for the Manuka Oval match.
Renshaw was notably overlooked in the Australia A squad that beat India A twice in a pair of tour games this month, and hasn't played a Test since February last year.
Debutant Nathan McSweeney was a surprise choice to open with Usman Khawaja for the first Test in Perth, picked ahead of Konstas, Cameron Bancroft and Marcus Harris, with Renshaw seemingly not in the frame.
But Renshaw's appearance in the Prime Minister's XI line-up gives him another chance to press his case for a Test recall if the door opens again at some point.
The 28-year-old made his 22nd first-class century in Queensland's drawn Sheffield Shield clash with Tasmania last week.
"Deleting a lot of apps and not reading any news has been a big one," Renshaw told AAP when quizzed on his form.
"It feels like every summer there is a circus about something and it is usually about the openers because Australian cricket wants another opener.
"I am really happy for Nathan. I think he is going to do a terrific job but for us openers I think (the decision) might have hurt a lot of us.
"We know how tough opening is and the satisfaction of batting for a long period of time is why we do the job, facing the toughest bowlers with a brand new ball at their freshest."
Boland is the most experienced player picked for the Prime Minister's XI and has a chance to underline his pink-ball credentials in Canberra, where the tourists are expected to field a strong batting line-up.
The tour game could also mark the eagerly anticipated return of India's regular Test captain Rohit Sharma, who has stayed at home to be with his family for the birth of his second child.
Victorian quick Boland is poised to take up any opportunity in the Test side but faces challenges from fellow contenders Lance Morris and Jhye Richardson, while Michael Neser is sidelined by a hamstring injury.
"The squad contains a mix of experience combined with some promising emerging players in Australian cricket," Australia's selection chief George Bailey said.
"The Prime Minister's XI match presents an opportunity for a highly talented squad to impress against a strong Indian team in their only pink-ball hit out prior to the second Test.
"We are utilising the opportunity to maintain Scott Boland's match fitness in his preparations as part of the Test squad.
"We thank the Prime Minister for his input into the squad, which sees some of the country's most exciting young cricketers mixed with some highly experienced players."
Morris and Richardson will get their own chances to impress with the pink ball in Western Australia's Shield clash with South Australia at Adelaide Oval, starting on Saturday.
NSW batter Jack Edwards will captain the Prime Minister's XI, which also features ACT Comets allrounder Hanno Jacobs.
PRIME MINISTER'S XI SQUAD: Jack Edwards (captain), Charlie Anderson, Mahli Beardman, Scott Boland, Jack Clayton, Aidan O'Connor, Ollie Davies, Jayden Goodwin, Sam Harper, Hanno Jacobs, Sam Konstas, Lloyd Pope, Matthew Renshaw, Jem Ryan.
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