The latest hit to the June 15 card is the fight featuring former light-heavyweight champion Mauricio (Shogun) Rua.
Rua was left without an opponent when fellow Brazilian Antonio Rogerio Nogueira withdrew due to injury.
There were reports Chael Sonnen would step in as a replacement but the UFC announced late Monday the fight was off.
"A whole bunch of circumstances probably came into play," said Wright. "In the end it was felt that the best thing to do was to let perhaps a Chael-Rua fight happen later but we would go with the card that we have in place."
The UFC said Rua will fight later this summer.
Wright couldn't comment on reports work-visa issues may have prevented Sonnen from coming.
The initial main event between interim bantamweight champion Renan Barao and Eddie Wineland on UFC 161 was lost weeks ago when Barao injured his foot.
Wright says the card still features two former Ultimate Fighter champions, a former Pride champion and the current main event between former light heavyweight champ Rashad Evans and Dan Henderson.
"Injuries are part of any sport and they're certainly part of this sport," Wright said when asked if the diminished card might damage the brand in Canada following a similar problem in Calgary at UFC 149 last year.
"I have every confidence that these guys, everybody on the card . . including the seven Canadians, will put on a great show and Winnipeg, Manitoba, will not be disappointed."
UFC 161 will feature 11 fights and the bout between Canadian light-heavyweight Ryan (Big Deal) Jimmo and Igor (The Duke) Pokrajac has been moved to the main card.
Injuries have also forced Isaac Vallie-Flagg and T.J. Waldburger off the card.
Henderson is making a return visit to Winnipeg but his last was in January and he says he didn't get out much.
Wright also highlighted the first-ever women's fight in Canada featuring Rosi Sexton and Alexis Davis.
"I think both of these athletes know they're making some history," he said. "That's the one that I'm really interested in watching."