Hardy scored a try before limping off at the Principality Stadium in the second half of the 40-24 victory.
Wales are confident Cardiff Blues' Tomos Williams will be fit again after suffering a hamstring injury in the opening victory against Ireland.
Wales hope fly-half Dan Biggar will be fit to face Italy on 13 March.
The Northampton half-back limped off against England and was replaced by Callum Sheedy who produced an impressive 13-point performance. Wales will find out next week if Biggar will be available.
At scrum-half, Wales should have three selection options in Gareth Davies, Tomos Williams and Lloyd Williams with nobody called up to replace Hardy.
His Scarlets' team-mate Davies came on as a replacement against England, while Lloyd Williams was called into the squad as cover for namesake Tomos, ahead of Rhys Webb.
"It's unfortunate for Kieran after a wonderful performance against England. He's worked particularly hard to improve aspects of his game, he's a very fit guy and we thought his performance was excellent, so it's unfortunate he's not in a position to back that up," Wales attack coach Stephen Jones told BBC Sport Wales.
"Where that leaves us is simple, we've got three scrum-halves left in the squad who are good to go. Tomos Williams is taking part in training so that's great for us."
"Biggs (Biggar) has got an injury he's nursing but we're very optimistic for next week (against Italy). We'll find out on Monday but we're pretty optimistic."
Jarrod Evans is the other fly-half in the squad if Biggar is unfit or rested for the trip to Rome.
Meanwhile Ospreys coach Toby Booth says the experienced Webb, who has slipped down the pecking order, is in "exceptional" form since his omission.
"All Webby can do for us is keep playing well, in the games for us in the last few weeks he's played exceptionally well.
"A week is a long time in politics, it's even longer in rugby so we'll wait and see," said Booth.