The 25-year old Brazilian has been on the sidelines for the past week and was expected to miss Madrid's match against Almeria on Saturday.
Marcelo, who was also announced as Real's third captain, said he was doing everything possible to make an early comeback.
"There's no fixed date but I'm training intensely and working hard to get back as soon as I can," Marcelo said.
"I'm the third captain of Real Madrid, and in addition to being a source of enormous pride, it's a responsibility, and I try to help the whole dressing room with the way I am."
Madrid's world record signing Gareth Bale said he is enjoying life in Spain, despite admitting to a 'slow start' at the Bernabeu.
"It's been great, since I've been here everybody's made me feel welcome - the players, the staff and everyone like that," Bale said.
"I've felt very comfortable straight away, obviously after a little injury and a bit of a slow start.
"I'm enjoying everything on the pitch now and I'm just looking forward to the rest of the season."
‘Even though Kevin Keegan was my boyhood hero, we never really saw eye-to-eye. That was an underwhelming time for me – I felt on the outside’: Newcastle cult hero reveals disappointment over how things went under King Kev
Alexander Isak puts uncertainty over his Newcastle United future to bed amid fresh PSG and Arsenal links
