The former England skipper underwent surgery in Auckland on Sunday and is expected to be sidelined for up to six months.
Martin Corry, who replaced Dallaglio on Saturday, has been named captain for Wednesday's clash with Taranaki while head coach Woodward has reserved special praise for the way Munster lock O'Connell performed against the Bay of Plenty.
"The whole party knows that with Lawrence out we need leadership," said Woodward.
"We lost a top player and somebody has got to step into his. I was especially pleased with O'Connell. He is a tremendous player."