The Uruguay winger suffered the setback while on international duty this week, limping out of his country's 1-0 win over South Korea just 24 minutes into the contest.
While an Atletico statement did not put a timeframe on Rodriguez's injury, he immediately becomes a major doubt for Saturday's La Liga clash with the UEFA Champions League holders at the Santiago Bernabeu.
It read: "The Atletico midfielder retired injured in the encounter between South Korea and Uruguay.
"Medical tests have determined he suffered a calf injury in the left leg.
"The player has today undergone medical tests in the FREMAP Majadahonda clinic. The diagnosis has determined that the Uruguayan suffering a hamstring injury, which is still being monitored."
Rodriguez may not have been at the forefront of coach Diego Simeone's thoughts for this weekend's match regardless as the winger has featured in just six minutes of action across Atletico's opening two games of the Liga season.