The defender twice required on-field treatment away to AZ Alkmaar before being replaced by Adam Montgomery after half an hour of the Europa League tie.
After missing the match at Ibrox and pulling out of the Scotland squad he was in from the start against Ross County but suffered another shoulder knock in the 48th minute with Montgomery sent on again.
If the injury requires surgery Taylor could be out for a couple of months with the hoops currently assessing the full extent of the injury.
The Daily Record reports:
Taylor aggravated a shoulder injury in the weekend win over Ross County and is a major doubt for the Group G opener in Seville. The left-back missed the Rangers game through the injury and now looks to have suffered a recurrence.
The Scotland international has been sent to see a specialist to try and get to the bottom of the issue, but it looks like the next European outing could come too soon. The positive news for the Hoops is that Ralston is now back in full training and will be available for the trip to Spain.
Adam Montgomery can come in as a direct replacement for just his second start as a Celtic player or Josip Jurnanovic can switch to left-back with Ralston returning at right-back.
Celtic fly out to Seville tomorrow with Postecoglou due to meet the media to preview the match.