Matfield joins fellow World Cup winner Bryan Habana on the Bulls' injury list, although at least the end is in sight for Habana after a hand operation. He is expected to play in the third or fourth tour match.
Matfield injured his right shoulder in the Bulls win over the Stormers two weeks ago - a recurrence of an injury that had kept him out of action for the two weeks prior to the game.
Bulls coach Frans Ludeke has given the captaincy of his side to Springbok scrum half Fourie du Preez for this weekend's clash with the Hurricanes, but hopes to have Matfield back for the clash with the Crusaders on 3 April.
"Losing Victor is a big thing for us and a huge loss. It is unfortunately the same shoulder and he will be out for three weeks," said Ludeke.
"He is a major influence in the team as a leader and as a player. Fortunately for us we have some good depth in the team and I am confident that Danie Rossouw, Bakkies Botha and Wilhelm Steenkamp will hold the fort well.
"The guys are upbeat regardless and we are leaving on the back of some good wins and have momentum on our side."