Carter, 24, was involved in a heavy collision immediately at the start of the clash in Kitakyushu and underwent several minutes of treatment on the field before being carried off on a stretcher.
The Welsh Rugby Union said on Tuesday he would take no further part in the tour and head home on Wednesday.
Wales lost 24-19, after being 19-7 up at halftime, extending their record losing streak to 18 matches.
The two teams meet again on Saturday in the second test at Misaki Park in Kobe.
--Reuters--