Vunipola started Saturday's 20-13 victory over Australia but was expected to drop to the bench against the Pumas following Alex Corbisiero's return from a knee problem.
"Mako is unfortunately struggling with a ligament strain to his knee and is not available for selection this week," Lancaster said.
Corbisiero's return from injury means he will start at loosehead against Argentina, with Joe Marler offering cover from the bench.
Lock Geoff Parling has recovered from the mild concussion he suffered in training last week, so Dave Attwood is among 10 players sent back to their clubs on Tuesday night.
Hooker Rob Webber is on standby for Saturday as Tom Youngs' wife is expecting their first child.
"There are a couple of changes to the squad with Geoff and Alex back and it's great they are back in the mix," Lancaster said.
"We have named an extended squad as we need a further 24 hours to assess one or two minor niggles in the build-up to the team announcement on Thursday morning."
Players released to their clubs: D Attwood (Bath), F Burns (Gloucester), K Eastmond (Bath), A Goode (Saracens), T Johnson (Exeter Chiefs), M Kvesic (Gloucester), H Thomas (Sale Sharks), H Trinder, (Gloucester), M Vunipola (Saracens), A Watson (Bath).