It is the latest injury blow to befall under-pressure manager Giovanni van Bronckhorst, who is already without eight first-team players, with his attack already depleted by the ongoing absences of Kemar Roofe, Tom Lawrence and Ianis Hagi.
Sakala was out of favour earlier in the season but has featured more regularly in recent weeks, starting his third match in a row at McDiarmid Park on Sunday as Rangers crashed to a 2-1 defeat at the hands of St Johnstone, before limping off late in the second-half.
However, the Zambian international will play no part in the matches against Hearts at Ibrox on Wednesday and St Mirren in Paisley on Saturday after Van Bronckhorst revealed the forward had picked up a minor injury.
The Rangers boss said: “Fashion had a scan yesterday [Monday]. He has a minor muscle injury and he will be out for a week which will rule him out for the last 2 games, but he will be back after World Cup for sure.”
Van Bronckhorst was also questioned on the situation with youngster Alex Lowry, who was posted missing from the squad in Perth on Sunday after making a late substitute appearance against Ajax in the Champions League defeat in midweek.
The 19-year-old only recently returned from a two-month injury lay-off.
"Alex is not in the squad – he is fit to play but is not in the squad,” Van Bronckhorst explained.