Full-back Maxime Medard has been called up as a replacement in the 33-man preliminary squad which will gather on Saturday to prepare for the competition.
Winger Vincent Clerc also picked up a minor injury on Friday while playing with his club side Toulouse and is doubtful.
The 22-year-old Dulin, who started France's last five games, picked up the injury during a French league game with his French club Castres on Thursday.
"With league games so close to the start of our competition, we have to expect this kind of news," France manager Philippe Saint-Andre was quoted as saying in the statement.
Medard, 26, returned last November after a knee injury he suffered during France's win over Scotland last year in the Six Nations ruled him out for eight months.
The Toulouse full-back, who was the first choice in the position during the 2011 World Cup, has 31 caps.
France's squad for their opening game in Italy on February 3 will be named on Monday.