Vunipola has not been included among the 33 players recalled by Eddie Jones to Pennyhill Park to begin preparations for Ireland as he has travelled back to Tonga for family reasons.
The 29-year-old was previously not selected for England’s opening weekend defeat by France but he returned for the Round 2 victory over Scotland at BT Murrayfield.
With Vunipola ruled out of England’s return to Twickenham, Joe Marler is set to return at loosehead prop with Ellis Genge resuming his role as a replacement.
Uncapped Obano has been called up to the training squad and the Bath Rugby man will be waiting in the wings for a potential first cap should Jones require his services.
Centres Manu Tuilagi and Henry Slade are both included in the training squad after recovering from injury, with the former on track to return after suffering with a minor groin niggle.
Luke Cowan-Dickie (Exeter Chiefs)
Tom Curry (Sale Sharks)
Tom Dunn (Bath Rugby)
Ben Earl (Saracens)
Charlie Ewels (Bath Rugby)
Ellis Genge (Leicester Tigers)
Jamie George (Saracens)
Maro Itoje (Saracens)
George Kruis (Saracens)
Joe Launchbury (Wasps)
Courtney Lawes (Northampton Saints)
Lewis Ludlam (Northampton Saints)
Joe Marler (Harlequins)
Beno Obano (Bath Rugby)
Kyle Sinckler (Harlequins)
Will Stuart (Bath Rugby)
Sam Underhill (Bath Rugby)
Harry Williams (Exeter Chiefs)
Elliot Daly (Saracens)
Ollie Devoto (Exeter Chiefs)
Fraser Dingwall (Northampton Saints)
Owen Farrell (Saracens)
George Ford (Leicester Tigers)
George Furbank (Northampton Saints)
Willi Heinz (Gloucester Rugby)
Jonathan Joseph (Bath Rugby)
Jonny May (Leicester Tigers)
Henry Slade (Exeter Chiefs)
Ollie Thorley (Gloucester Rugby)
Manu Tuilagi (Leicester Tigers)
Jacob Umaga (Wasps)
Ben Youngs (Leicester Tigers)
Alex Mitchell (Northampton Saints)