Costelow limped off during the 26-23 defeat by Scotland in their last game last month, but remains with the squad as he recovers from an ankle injury.
"Sam is not quite ready for this week. We're hoping he will play a part in the Six Nations, but not this week," assistant coach Matt Sherratt told a Monday press conference.
Over the last few days, Wales have also had lock Rhys Davies and loose forward Taine Plumtree ruled out for the remainder of the tournament through injury.
Dragons' uncapped utility forward Ryan Woodman has been called up as a replacement, while Cardiff prop Keiron Assiratti - who was initially named in the Six Nations squad before being withdrawn through injury - has returned.