Hooker Owens has followed his Scarlets colleagues - fly-half Rhys Priestland (Achilles) and centre Scott Williams (shoulder) - in being ruled out of the two-Test trip.
Owens' withdrawal from the Japan trip was confirmed by the Welsh Rugby Union.
He took a blow to his neck during the Scarlets' RaboDirect PRO12 play-off defeat against Ulster in Belfast last Friday, which affected a nerve in his arm.
Uncapped Newport Gwent Dragons hooker Sam Parry was called into the Wales training squad earlier this week, with tour head coach Robin McBryde due to announce his final 27-man tour party next Tuesday.
Wales, who play Japan in Osaka on June 8 and then Tokyo seven days later, were already without 15 players named in the British and Irish Lions squad for next month's tour of Hong Kong and Australia.