Alongside his BBC commitments, Jenas has a relationship with TNT Sport, formerly BT Sport. He has provided commentary for its football coverage, and presented its E Sport programming.
Jenas is not scheduled to appear on air again for a broadcaster for a number of weeks, it is understood.
His departure is the latest in a number of recent difficulties for the BBC. In July, Huw Edwards, the News at 10 presenter, pleaded guilty to possession of 41 indecent images of children, having initially been suspended from frontline duties in July last year.
An internal inquiry had been launched following reports that Edwards paid £35,000 to a man, who was 17 when the alleged relationship began, in exchange for sexually explicit images.
The BBC has asked Edwards to return the £200,000 of salary he received in the month following his arrest last November.
The corporation is also dealing with internal unrest over its HR system, which staff have claimed is not fit for purpose. Whistleblowers who came forward to raise concerns about Edwards said they felt their their complaints had been “swept under the carpet”.
The BBC has also been dealing with an ongoing Strictly row after former contestant Amanda Abbington accused her ex-dance partner Giovanni Pernice of abusive behaviour – claims he has resolutely denied.
Both parties are awaiting the findings of a BBC inquiry into the claims.