The Colombia international sustained the problem during Real's 3-0 defeat of Celta Vigo in La Liga on Saturday.
Rodriguez had to be replaced by Alvaro Arbeloa in the 53rd minute and the extent of the injury was revealed on Monday.
"Following tests carried out on James Rodriguez by the Real Madrid Sanitas medical services, he has been diagnosed with a grade one muscular injury in the inner calf of his right leg," a brief statement read.
"His progress will be monitored."
A grade one injury is the least serious of its kind and, although Real did not put a timescale on Rodriguez's recovery, he is expected to miss the UEFA Champions League clash with Ludogorets on Tuesday.
Rodriguez, who has scored nine goals in all competitions so far in his debut season at the Santiago Bernabeu, could also be a doubt for the trip to Almeria in La Liga on Friday.
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
