The club confirmed on Tuesday evening that Asofa-Solomona has required a minor procedure on his finger after it was dislocated in last Saturday's loss to Newcastle.
The surgery isn't expected to place the Storm form out of action for long, with the club hopeful the 27-year-old will be available to suit up for next weekend's trip to BlueBet Stadium to face Penrith.
The Storm will re-assess their hampered prop ahead of the Round 23 bout, with Asofa-Solomona to be subject to fitness tests.
Smith will be sidelined for up to three weeks after suffering an adductor strain in the eight-point defeat to the Knights.
The blow will mean a best-case scenario for Smith is a Round 24 return against the Canberra Raiders, with the Storm winger expected to miss the coming matches against Parramatta and Penrith.
Duo Elisea Katoa (eye) and Aaron Pene (ankle) are in the mix to feature for the Storm this weekend following recent ailments, with the pair named on the interchange and reserves list respectively for Friday's matchup with the Eels.
That clash will take place at Marvel Stadium at 8:00pm (AEST).