The 24-year-old Wales international, who is only three games into a comeback from a shoulder injury which kept him out for three months, tore a thigh muscle during Saturday’s 1-0 Sky Bet Championship defeat at QPR.
Coleman told the club’s official website: ‘Jonny will be out for a month. It is a grade two tear in his quad.
‘That’s disappointing because it has been a tough season for Jonny, very stop-start. I can’t get him fit and keep him fit and that’s a shame because he is such a good player. And in full flow as a Sunderland player the supporters would love him.
‘We haven’t managed to see that because unfortunately he has had bad luck.’
Coleman already has Robbin Ruiter, Tyias Browning, Paddy McNair, Darron Gibson and Duncan Watmore on the long-term casualty list, although Gibson is back in light training after a groin problem.
Watford boss Javi Gracia does not think Abdoulaye Doucoure's form will be affected by his omission from France's latest squad.