The Congo captain moved to Molineux from Reims last August for an undisclosed fee.
But the 28-year-old has only made 11 first-team appearances and none since a 1-0 defeat at Brighton in mid-October when he was substituted at half-time.
Bastia are currently 17th in the French top-flight, having won five of their 20 games so far this season.
"The deal has been done for him to join Bastia on loan until the end of the season, and then we will be able to revisit the situation and see what the future holds," Wolves sporting director Kevin Thelwell told the club website.
Head coach Paul Lambert is keen to reduce the size of his squad in January.
Dutch forward Ola John left Wolves on Friday, cutting short his loan spell from Benfica to join Spanish club Deportivo La Coruna on loan for the remainder of the season.
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Wolves midfielder Prince Oniangue has joined French club Bastia on loan until the end of the season.