The Colombia international required surgery after damaging the fifth metatarsal in his right foot during Wednesday's 2-1 La Liga victory over Sevilla, in which he scored the opener.
James is consequently set for a lengthy spell on the sidelines, but the 23-year-old remains in positive spirits.
"I will recover and come back stronger than ever," he posted on Twitter.
"The messages [I have received] are very supportive. Thank you!"
James moved to the Santiago Bernabeu side in a high-profile move from Monaco after impressing at last season's World Cup, where he collected the Golden Boot award.
The former Porto star has scored 12 goals in all competitions for Real Madrid this season.
