Bright, who was appointed captain after Leah Williamson suffered an ACL injury and then led the Lionesses to a runners-up finish at this year's Women's World Cup, pulled out of the squad due to a knee injury and will remain with Chelsea for treatment.
Asked about Bright's injury, Wiegman told reporters: "She wasn't available for Chelsea before, so we knew. We always know what our next step is, we're always thinking of scenarios when someone is not available.
"Mary will captain the team tomorrow."
England, who were beaten 3-2 by Belgium in their last Nations League game, are third in Group A1 and must beat leaders Netherlands at Wembley if they are to have a chance of winning the group and progressing to next year's finals.
"(The Netherlands) have an experienced team, most of their squad has played in big occasions. They'll be excited to be there and to play at Wembley," Wiegman said.
Friday's game could also see Beth Mead make her first appearance for England after a lengthy spell on the sidelines due to an ACL injury.
Mead missed the World Cup but has made her return to club football for Arsenal, scoring twice in a 3-0 win over West Ham United in the Women's Super League on Sunday.
"We have lots of players up front who are in good form and I am really excited that she is back. First of all, as a person after what she has gone through in the last year. She always smiles and connects with everyone," Wiegman said.
"It is good to have her back but it starts with her performances. At Arsenal, she is just building her minutes and you can tell she is in a good place. Her last game was incredible, her second goal in particular was really nice.
"It is like she hasn't been away. She feels good and trains really well. We have lots of hard decisions to make ahead of Friday."
England will end the group stage with a trip to Scotland on December 5th.
