Higuain is out of action with a slipped disc in his back and Mourinho compared his absence to that of Brazilian playmaker Kaka, who has been out since the start of the season with a knee problem.
"We were missing (Kaka) for six months and we built a team," Mourinho said at a press conference prior to Monday's trip to Getafe.
"Now we have to build a team without Higuain. The team has to adapt to the circumstances. Some players will have to play in positions that are not theirs, in a different system."
Mourinho added that Higuain "will have to have an operation, without any doubt".
Higuain, who typically starts in attack for Real alongside Cristiano Ronaldo, has been unable to play since the end of November.
Real revealed at the beginning of December that the 23-year-old had sustained a slipped disc that could necessitate an operation, which would keep him out of action for a further two months.