All Blacks Doctor Deb Robinson said McCaw, who was due to play his 100th Test against Japan, had suffered a minor calf strain in his left leg, Muliaina had a tight right hamstring and Dagg had a right abdominal strain.
"It was a bad day at the office as far as injuries are concerned but the good news is that all the injuries are not serious.
"There would be risk of further injury to these players if we let them play so we have withdrawn them. We will now concentrate on their rehabilitation with the aim of getting them ready to resume training next week to prepare for the France Test."
With World Cup rules around replacements she did not want to risk a muscle tear which would keep the players out of the rest of the competition.
She said each of the players had improved overnight but the team management had adopted a conservative attitude in keeping the players on the bench.
"We've now got essentially four days until we start training next week so we feel really positive about getting them to a position where they can train next week.''
Her decision was nothing to do with next week's game against France, a tougher opposition than Japan.
"I just face the facts that I've got in front of me and that is that these guys have got minor muscle injuries and if they play tomorrow night and they get a tear then they could be out of the competition.''
The injuries have forced a reshuffle of the starting XV and the reserves bench for the Test against Japan.
Isaia Toeava will now start at fullback, Adam Thomson will shift to openside flanker and Victor Vito comes off the bench to start at number eight.
Lock Anthony Boric comes onto the bench to replace Vito.
All Blacks coach Graham Henry said: "It's disappointing to have the players unavailable, especially Richie and Mils who were both looking forward to playing against Japan. But injuries are something that we all have to deal with and it's great that we have versatility in the squad so Isaia is able to slot in at fullback."
The revised All Blacks team to play Japan is now as follows:
Starting XV:
1. Tony Woodcock (77 tests)
2. Keven Mealamu (86) - captain
3. Owen Franks (25)
4. Brad Thorn (53)
5. Sam Whitelock (19)
6. Jerome Kaino (42)
7. Adam Thomson (22)
8. Victor Vito (9)
9. Andy Ellis (21)
10. Colin Slade (6)
11. Richard Kahui (13)
12. Ma'a Nonu (61)
13. Conrad Smith (49)
14. Cory Jane (27)
15. Isaia Toeava (33)
Reserves:
16. Andrew Hore (56)
17. John Afoa (34)
18. Ali Williams (67)
19. Anthony Boric (21)
20. Jimmy Cowan (48)
21. Piri Weepu (50)
22. Sonny Bill Williams (8)
