Cardiff Blues expect Wales back-rower Josh Navidi will be out of action for six weeks after he suffered a hamstring injury at the World Cup.
Navidi,28, injured his hamstring during Wales' 20-19 quarter-final win over France.
"Navs has a hamstring injury that'll take a bit of time to get right," said Mulvihill.
"But he's had a big year internationally and it's important we give him time to mend."
Mulvihill added: "He'll spend a little extra time rehabbing compared to the other boys in Japan."
Blues wing Owen Lane was added to Wales' World Cup squad after Navidi was ruled out of the tournament.
Lane will start against New Zealand in Friday's bronze final and Mulvihill welcomed the call-up for the 21-year-old.
"We want as many players as possible to graduate from our academy to the Blues and into a red jersey," said Mulvihill.
Samoa centre Rey Lee-Lo is back from Japan to face Munster at the Arms Park in the Pro14 on Saturday.
Lee-Lo, who was suspended for a dangerous tackle in Samoa's World Cup opener against Russia, will start instead of New Zealand-born Tonga under-20 cap Willis Halaholo, who is now qualified to play for Wales on residency grounds.
Mulvihill hopes to have one or two Wales internationals back for the Leicester game in round two of the European Challenge Cup in November, depending on their work-load in the World Cup.