The 28-year-old joined the Midlands side from Reims in a £2m deal as part of a 13-player spending spree by the club's new Chinese owners Fosun International.
Oniangue made 11 starts for Wolves but has not played since mid-October following the arrival of Paul Lambert, who is on a mission to trim down his senior squad to 23 players this month.
"Prince was unfortunate in picking up an injury earlier in the season and being sidelined for a spell," said Wolves sporting director Kevin Thelwell.
"Since he has returned to fitness, the team has been playing very well and he has been unable to force his way back into the starting lineup.
"He is at an age where he really needs to be playing games, and, with his profile in France, there has been plenty of interest from different clubs.
"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."
Oniangue becomes the fourth player to be released by Lambert this month, with Cameron Borthwick-Jackson returning to parent club Manchester United, Ola John being sent out to Deportivo La Coruna and Connor Hunte having his contract terminated.
Paul Gladon, a £1m summer signing from Heracles, is thought to be next in line for the chop after making just two appearances all season.