The experienced centre-half suffered an Achilles injury during the recent 1-0 win at Derby and will not be fit until May.
Lions physio Bobby Bacic told the club website: "Danny will effectively be ruled out for the rest of the season.
"There are only just over six weeks of the season left and by the time Danny is due to recover from his Achilles injury he will be short of match fitness.
"He is currently in a protective boot for another three weeks so he is limited in the football-specific fitness work he can do, and even when he comes out of the boot he will be doing low level loading for the following two weeks."
Club captain Paul Robinson has returned to the side in Shittu's absence and will continue at Leeds on Saturday.