The two neighbours convene at the iconic Olympiastadion, with the winner of their last-16 tie meeting either England or Slovakia in the quarter-finals.
Match preview
On course to upset the tournament hosts and qualify as Group A winners, Switzerland were denied victory by a late Germany goal in last Sunday's final group fixture, but they nonetheless reached the knockout rounds unbeaten.
Dan Ndoye put Die Nati ahead after 28 minutes in Frankfurt, but Niclas Fullkrug's stoppage-time equaliser left them with five points on the board - enough to finish just below their next-door neighbours, and ahead of both Hungary and Scotland.
Murat Yakin's men followed an opening win with a less impressive stalemate against Steve Clarke's side, and after running the Germans close, they have now made the elimination phase at each of the last six major tournaments: that streak dates back to 2014, and the only European nation on a longer such sequence is France, with seven.
However, excluding shootouts, Switzerland have failed to win any of their seven previous last-16 matches at either the Euros or World Cup outright, progressing to the quarter-finals on just one occasion.
Three summers ago, a stirring comeback took favourites France to penalties, in which the Swiss then prevailed, and overcoming that psychological hurdle may stand them in good stead for Saturday's showdown in the German capital.
Though Switzerland have lost only once in their last 13 European Championship matches, that sole setback was a 3-0 defeat to Italy at Euro 2020 - and since winning a World Cup qualifier in 1993, they are winless in 11 games against the Azzurri across all competitions.
While clearly holding an historical advantage over their next opponents, Italy still bear the scars of two draws between the nations that ultimately saw them miss out on a place at Qatar 2022.
A notorious pair of penalty misses by midfield metronome Jorginho cost La Nazionale dearly in both qualifying matches, and the European champions have never quite recovered their equilibrium since then.
After reaching Euro 2024 by narrowly avoiding a playoff, Italy edged out Albania in their opener, before being put to the sword by a fluent Spain side in Gelsenkirchen; then, Monday night's dramatic draw with Croatia carried them through Group B by a whisker.
Trailing deep into eight minutes of second-half stoppage time, substitute Mattia Zaccagni stole a precious point with his brilliant last-gasp strike and cruelly broke Croatian hearts in the process.
As it turned out, Luciano Spalletti's side would have been eliminated if they had ended up with just three points and a negative goal difference, so Zaccagni's moment of magic effectively kept their title defence alive.
Notwithstanding their woes in World Cup qualifying, the Azzurri have reached the quarter-finals of every Euros since 2004, and that will now be their minimum aim in what is generally perceived as the weaker half of the draw.
Should they make it past the Swiss, a possible reprise of their Euro 2020 decider versus England could then be on the cards: like Gareth Southgate, Italy's maverick manager is under increasing pressure from an expectant audience at home and in the media.
Both men will expect their players to step up a gear in the win-or-bust knockout phase, during which Spalletti's spell as national boss will truly be judged.
Switzerland European Championship form:
W
D
D
Switzerland form (all competitions):
W
W
D
W
D
D
Italy European Championship form:
W
L
D
Italy form (all competitions):
W
D
W
W
L
D
Team News
Switzerland will be forced to make at least one change to their starting XI on Saturday, as Leonidas Stergiou is set to come in for the suspended Silvan Widmer, who picked up his second booking of the tournament against Germany.
Forward pair Ruben Vargas and Zeki Amdouni are both pushing for promotion from the bench - with London-born rookie Kwadwo Duah in contention too - but Breel Embolo has now made his first international start after a long injury layoff and should continue up front.
In midfield, captain Granit Xhaka partners Remo Freuler, who has set up three goals in his last four European Championship appearances: the latter is one of several Serie A players in the Swiss squad, including Inter Milan goalkeeper Yann Sommer.
Meanwhile, Italy must also react to a first-choice defender's suspension, as Riccardo Calafiori received two yellow cards during the group phase and will miss out on a meeting with Bologna teammates Freuler, Ndoye and Michel Aebischer.
Francesco Acerbi and Giorgio Scalvini were left at home due to pre-tournament injuries, so Gianluca Mancini is favourite to step into the Azzurri's defence: whether he features at the heart of a back four or a three-man rearguard remains to be seen, as Luciano Spalletti has fluctuated between the two systems of late.
Elsewhere, Gianluca Scamacca may return at the expense of fellow striker Mateo Retegui - neither has scored at these finals thus far - and Giacomo Raspadori could make way for either Federico Chiesa or Monday's hero, Mattia Zaccagni.
Switzerland possible starting lineup:
Sommer; Schar, Akanji, Rodriguez; Stergiou, Xhaka, Freuler, Aebischer; Ndoye, Vargas; Embolo
Italy possible starting lineup:
Donnarumma; Darmian, Mancini, Bastoni; Di Lorenzo, Barella, Jorginho, Pellegrini, Dimarco; Chiesa, Scamacca
We say: Switzerland 1-1 Italy (Switzerland win after extra time and penalties)
A cautious contest is to be expected between two teams that know each other so well, having met in several big games and with many Swiss stars plying their trade on the Italian peninsula.