Mularkey said Monday the injury is serious but not as significant as the Titans had feared.
Spain was carted off the field in the second quarter of a 34-26 loss to Indianapolis.
Cornerback Perrish Cox is in the concussion protocol and likely will not be cleared to play Thursday night when the Titans (3-4) host the Jaguars (2-4).
Mularkey says coaches will look options to replace both Spain and Cox in the starting lineup. Brian Schwenke replaced Spain, while the Titans rotated both Valentino Blake and Brice McCain after Cox's injury.