A tense penalty shootout win over Colombia in the previous round secured the Swiss passage into the final eight for the first time since 1954 as they take on La Albiceleste in Kansas City on July 12.
Argentina's own last 16 clash was packed with controversy, as they came from 2-0 down to beat Egypt 3-2, in a game dominated by VAR calls and bold decisions from match referee François Letexier.
Egypt saw a goal ruled out following a lengthy VAR check and captain Mohamed Salah was denied a penalty in the closing stages.
Argentina talisman Lionel Messi missed his own penalty in the game - the second time he's failed to convert from the spot at this World Cup - and Swiss head coach Murat Yakin fired a cheeky comment over his expectation to concede a spot kick against the holders.
"We’re playing against the world champions. There’s nothing better than having this opportunity. But it’s also been clear, over the last two matches, that Argentina are vulnerable.
"Our goalkeeper has already started practicing for penalties. We know Argentina could be awarded a penalty."
Argentina have been awarded the most penalties so far in the tournament, with Messi missing two, and Lautaro Martinez converting the other one for Lionel Scaloni's team.
Despite his struggles from 12 yards in recent games, Scaloni has confirmed there are no plans to remove penalty duty from his captain at the World Cup.