Alves had to be replaced with around 15 minutes remaining in Rangers’ 3-1 Betfred Cup win over Partick Thistle in mid-week.
But STV is reporting that the Portuguese veteran has been told to rest and may be out for a fortnight.
Alves’ injury is likely to mean a baptism of fire for young defender Ross McCrorie, who replaced the Portugal international on Tuesday night.
Rangers manager Pedro Caixinha hailed the teenager after the victory over Partick, asserting that he would be ‘one of the best centre halves in history’ for both Rangers and Scotland.
He is likely to partner Fabio Cardoso in central defence.
Rangers are also missing captain Lee Wallace and fellow defender Danny Wilson, while there were fears over Declan John’s fitness after the on-loan Cardiff City defender also limped out of the Partick clash.
Jordan Rossiter and Niko Krancjar also miss out but Wes Foderingham will return in goal and Kenny Miller could make a comeback after sitting out the match on Tuesday night.