The 26-year-old was stretchered off the pitch following a tackle from Delon Armitage.
The injury has ruled the Scarlets back out of September’s Rugby World Cup, and it is unclear how long he will be out of play.
A release on the WRU website read: “Morgan Stoddart has had successful surgery on his broken leg and will return to Wales from London tomorrow.
“The good news about Morgan is that he has come through surgery successfully and he will now begin his rehabilitation programme back at the Scarlets,” WRU medical manager Prav Mathema added.
Wales face England in a return World Cup warm-up match in Cardiff this weekend.