Dagg travelled with the team to Suva but will only take part in promotional activities.
The 28-year-old outside back had a knee operation in mid-March but played 40 minutes of club rugby last weekend and declared himself ready to resume playing for the Crusaders.
Coach Scott Robertson disagreed and left him out of the match in Suva, where the Crusaders will be looking to retain their perfect record this season with a 12th consecutive win.
That leaves Dagg with just two more Super Rugby matches to prove his match fitness before Steve Hansen names his squad for the British and Irish Lions series on June 8.
Photo: Photosport Crusaders fullback Israel Dagg