"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.
The Welsh flyer may be available for selection by the time Wales travel to Italy later this month but for the moment, head coach Warren Gatland will have to shuffle his pack.
Cardiff Blues' Tom James and Chris Czekaj are options for Gatland who may also face a selection headache in the forwards as they await scans on Andy Powell's bruised shoulder.
Powell was given the nod to start at No. 8 but was replaced in the first half by Ryan Jones and faces an anxious wait to discover the extent of his injury.