The Irishman was ruled out after suffering a recurrence of an old groin injury in training on Wednesday.
The Lions' medical team had hoped he would recover in time to play in the warm-up matches, but an Auckland-based specialist confirmed on Thursday that the injury was worse than they had thought.
The Lions turned to Shaw, who was called into the England World Cup squad as a late replacement for Danny Grewcock, ahead of other possible candidates Brent Cockbain and Robert Sidoli of Wales.
Shaw, who was preparing for Martin Johnson's testimonial match this weekend, plans leaving for New Zealand this evening, to arrive on Saturday.
He said: "I am absolutely delighted but feel for Mal and wish him well in his recovery.
"It is a great honour to be involved with the Lions, and to be honest it is all just sinking in but it will be fantastic to get out there and I am looking forward to the challenge that we will face in New Zealand."