Millward starts for Ospreys while Andy is among Glasgow's replacements.
Millward is one of eight changes to the side after last Friday's win over Ulster as coach Lyn Jones is hit by international call-ups.
Fly-half Shaun Connor, who has twice fractured his shin, makes only his second start of the season.
Andy Newman and James Bater form a new second row partnership to cover for Brent Cockbain and Jonathan Thomas.
Thomas is on the bench, but Cocknbain and fellow Wales squad members Sonny Parker, Adam Jones, Shane Williams and Richie Pugh are rested ahead of the Six Nations opener on 5 February.
Prop Paul James has been training with the Wales squad following Duncan Jones' broken thumb, but coach Mike Ruddock has released him for the trip to Scotland.
Ospreys: A Durston; S Terblanche, D Bishop, E Seveali'i, P Mackey; P Connor, R Rees; P James, B Williams (capt), A Millward, A Newman, L Bateman, J Bater, R Jones, S Tandy.
Replacements: R Hibbard, C Griffiths, J Thomas, A Lloyd, J Spice, M Jones, D Tiueti.