The Ibrox club were due to play the Portuguese giants in the Eusebio Cup on Friday in Hamilton, Ontario.
But Benfica have pulled out without any explanation.
The sudden cancellation has angered Rangers who are now taking legal advice. The club has also apologised to fans who have booked travel to and accommodation in Canada.
Manager Pedro Caixinha had hoped to use the trip to help bond the squad after a difficult few days.
Following the defeat by Celtic last weekend tempers had reportedly flared at a team meeting, with veteran striker Kenny Miller sent to train with the club’s development squad.
Rangers released a statement on Saturday night to confirm that the match was off.
“Rangers’ match against Benfica, scheduled for Friday October 6, has been cancelled,” said the release.
“Rangers were due to fly out to Canada for the match – scheduled for Tim Hortons Field in Hamilton – on Tuesday 3 October but were informed of Benfica’s decision only hours ago.
“The organisers, Elite Soccer Entertainment, have apologised but Rangers will be expressing their displeasure on behalf of themselves and their supporters in the strongest possible terms.
“Rangers also wish to apologise to those fans, who had made arrangements to travel, and those in Canada, who were looking forward to the match.
“Rangers will take legal advice before commenting further.”