A specialist will review his injury on Monday when a formal assessment of when he may return to play will be made, but it is hoped he will make a speedy recovery.
"Morgan has broken a metacarpal bone in his right hand and will have a consultation with a hand surgeon when he reports back to the Wales camp on Monday," said Wales physiotherapist Mark Davies.
"It is too soon to say how long he will be in recovery but it is hoped that he will be back in contention for selection soon and be able to play a further part in the Championship.
"We will have a clearer idea of when he may return to play by Monday."
Elsewhere the Wales squad have reported a variety of bumps and bruises after the hard fought loss to England, with Wasps No8 Andy Powell noteably leaving the field with a bruised shoulder in the first half of the game, and a full injury assessment will be available at the start of the week.
No further players have been added to the Wales squad to date.