Murray, 26, suffered a broken hand in the team’s game against the Philadelphia Flyers last Saturday and is expected to miss three to four weeks.
Texier, 20, hurt his knee in the same game against the Flyers and is slated to be sidelined for two to four weeks.
Murray, the second-overall pick in the 2012 NHL Draft, has four points in 10 games this season. He is coming off a 2018-19 campaign when he racked up a career-high 29 points across 56 games.
Texier, meanwhile, has three points in 11 games during 2019-20.
The rookie was selected in the second round of the 2017 NHL Draft (45th overall) by the Blue Jackets.