Sean Cronin has replaced Best at hooker, with Leinster's two-time European Champions Cup-winner making a belated first start in the Six Nations at the age of 32.
Although he has been capped 67 times by Ireland, 58 of Cronin's appearances have come off the bench - a record for any Ireland replacement.
Best's absence means the Ulster front-row forward will miss just his second Six Nations match in the last 63 - a run dating back to 2007 - with O'Mahony captaining the team for the first time in the Six Nations although the blindside flanker first led Ireland on their 2013 tour of North America.
Meanwhile Connacht flyhalf Jack Carty could make his Test debut off the bench, with Joey Carbery sidelined by a suspected hamstring problem.
Italy, coached by former Ireland fullback Conor O'Shea, are on a woeful run of 19 straight defeats in the Six Nations and it has become increasingly commonplace for their European rivals to rest senior players for matches against the Azzurri in a bid to keep them fresh for sterner challenges ahead.
Schmidt, however, made just four changes - all in the pack - to the run-on side that beat Scotland 22-13 last time out, with the New Zealander selecting first-choice halfback pair Conor Murray and Jonathan Sexton when he announced his starting XV on Friday.
"Joey Carbery has a hamstring strain and wouldn't really have been available," said Schmidt, who is guiding reigning champions Ireland in his last Six Nations as their coach before standing down after this year's Rugby World Cup in Japan.
"It would have been too great a risk for him to feature.
"We probably would have started Johnny (Sexton) anyway to be honest. He's had one game and 23 minutes since the Munster game. He's had very little game time.
"And Joey has had a lot of game time and played the bulk of the game in Edinburgh."
Schmidt, explaining the changes to the pack, added: "Some of it is just to offer an opportunity, it's to reward the effort we are seeing in training and in games so far.
"And at the same time it does offer us a little bit of an opportunity to give some guys a weekend off, the likes of Rory and James Ryan, Cian Healy - those guys have probably had the most game minutes so far."
Ireland head into this weekend's third round of matches fourth in the table after an opening defeat by England was followed by victory away to Scotland.
Play starts on Sunday at 17:30 SA time.
15 Jayden Hayward; 14 Edoardo Padovani, 13 Michele Campagnaro, 12 Luca Morisi, 11 Angelo Esposito; 10 Tommaso Allan, 9 Tito Tebaldi, 8 Braam Steyn, 7 Maxime Mbanda, 6 Jimmy Tuivaiti, 5 Dean Budd, 4 Federico Ruzza, 3 Simone Ferrari, 2 Leonardo Ghiraldini (capt), 1 Andrea Lovotti
Substitutes: 16 Luca Bigi, 17 Cherif Traore, 18 Tiziano Pasquali, 19 David Sisi, 20 Alessandro Zanni, 21 Guglielmo Palazzani, 22 Ian McKinley, 23 Tommasso Castello
15 Rob Kearney; 14 Keith Earls, 13 Chris Farrell, 12 Bundee Aki, 11 Jacob Stockdale; 10 Jonathan Sexton, 9 Conor Murray; 8 Jordi Murphy, 7 Sean O'Brien, 6 Peter O'Mahony (capt); 5 Quinn Roux, 4 Ultan Dillane; 3 Tadhg Furlong, 2 Sean Cronin, 1 Dave Kilcoyne
Subtitutes: 16 Niall Scannell, 17 Jack McGrath, 18 John Ryan, 19 Iain Henderson, 20 Josh van der Flier, 21 John Cooney, 22 Jack Carty, 23 Andrew Conway