Bresnan was forced to pull out of the Roses match with a pectoral injury moments before it was announced that he had been handed an England recall as part of their 14-man squad for the one-off T20 at Edgbaston.
Martyn Moxon, Yorkshire’s director of cricket, said: “Tim picked up the injury during the last week or so. He tried bowling in the pre-match warm-up at Old Trafford but we decided not to risk him in the Roses game.
“He probably won’t bowl now until Thursday or Friday, but the signs are that he should be okay for the England match.
“He is receiving treatment with us and we hope that the injury will clear up within three or four days.”
Bresnan last played international cricket in March when he was part of the side that lost to Netherlands in the World T20.
The 29-year-old lost his Test place after the Ashes tour and has not featured in one-day cricket since the three-match series in West Indies last winter.
But some good T20 showings for Yorkshire have gained their reward, with Bresnan having scored 175 runs in 10 T20 games at 43.75 and taken nine wickets at 29.11.
He is one of four players in England’s T20 squad not involved in the current one-day series against India, along with Surrey batsman Jason Roy (the only uncapped inclusion), Ravi Bopara and James Taylor.
With England not scheduled to play another T20 until next June, they could use Sunday’s match as a chance to look at fringe candidates for the World Cup.
Bresnan could yet come into contention for that tournament, particularly with England having struggled to find a successful ODI formula.
Looking ahead to Sunday’s match, James Whitaker, the national selector, said: “This one-off NatWest T20 provides us with an opportunity to look at players who have impressed recently in domestic cricket and gives them a chance to test themselves on the international stage against high-quality opposition.
“I would like to wish Eoin Morgan and his squad all the very best against a strong Indian side.”
England squad (from): Eoin Morgan (captain), Moeen Ali, Ravi Bopara, Tim Bresnan, Jos Buttler, Steven Finn, Harry Gurney, Alex Hales, Chris Jordan, Joe Root, Jason Roy, James Taylor, James Tredwell, Chris Woakes.