The two nations meet in Sao Paulo tonight with a quarter-final clash against either Belgium or the USA awaiting the winner.
While claiming that the Swiss are capable of causing an upset, Mehmedi is aware that he and his teammates face a difficult task against the South Americans.
"I know the quality and potential of this team. If we defeat Argentina, we write a piece of World Cup history and many people in Switzerland will be proud of the team," he is quoted as saying by BBC Sport.
"I even think such success would see the world take notice, but we are not naive. It will take an absolutely top performance of each one of us, and I assure you everyone will do everything we can to provide these and tearing for Switzerland."
Mehmedi has scored one goal in three games for Switzerland so far at the World Cup.