The former Liverpool and England captain took his first steps into management when he replaced Graeme Murty at Ibrox.
The defender suffered an injury to his knee during a training session on Wednesday and he will now miss the end of season run as the Light Blues bid to win a domestic Treble.
The 25-year-old has been a go-to at the back for Brendan Rodgers this season, making 40 appearances for the club. Scales initially joined the Hoops from Shamrock Rovers in August 2021.