Sharma, who had made a well-crafted half-century in India's 133-run hammering of England in the second game, suffered a fracture on the middle finger of his right hand.
Murali Vijay has been picked as Sharma's replacement for the rest of the series.
Sharma's injury has turned out to be India's biggest worry going into the third One-dayer.
The first ODI in Bristol was abandoned without a ball being bowled and India hammered the hosts under the Duckworth/Lewis method in the second game in Cardiff to take a 1-0 lead in the five-match ODI series.
Having recorded his first century outside the sub continent with a blazing 75-ball 100, Suresh Raina will look to carry on in same fashion while Ravindra Jadeja was the pick of the bowlers in the second game.
The two teams have played at Trent Bridge earlier this summer and there were two resultants from that first Test here.
First, the pitch for that match was deemed poor by the match referee David Boon and the groundsman received an official warning from the ICC. There was nothing in it for the bowlers who toiled hard as the batsmen mostly tailenders from both sides made merry.
If a similar pitch is doled out for this ODI match though, no one will be complaining as the weekend crowd will get to see a high scoring encounter, hopefully with the top-order scoring this time around.
The second resultant though had more far reaching consequences on how that Test series panned out. The Ravindra Jadeja-James Anderson clash has only recently receded from memory and this match has come about to enliven the episode again.
The Indian management had pressed ahead in their bid to get the fast bowler banned for allegedly pushing Jadeja, so much so that they lost focus on the task at hand and lost the series 1-3 despite taking a 1-0 lead.
As the two teams walk through that infamous narrow corridor of the pavilion at Trent Bridge, they will feel differently about that episode. India will feel that they have a point to prove. The format has changed, and as was apparent in Cardiff, they clearly hold the edge over England in limited-overs cricket.
They cannot lose steam and instead must go for jugular, for this is not about revenge for the Test series loss.
Instead this is about building up to the ODI World Cup and registering as many consistent performances as they can in the next six months.
In that light, India's success at Cardiff was a great starting point. Four of the six batsmen scored runs. Among them, it was vital for Sharma and Ajinkya Rahane to come good. While the former has now been ruled out, the clock was beginning to tick on the latter's role as the number four bat. In scoring 41 runs, Rahane has bought some time for himself and reduced one area of concern for the management.
Indian skipper Mahendra Singh Dhoni had confirmed after the match that Raina will continue to bat at number five and this declaration sews up the batting order. The worrying bit is about Shikhar Dhawan's form and that Virat Kohli has not been able to buy a run on this tour.
While India will surely be patient with their vice-captain, the same cannot be said about the left-hander. In New Zealand, Dhawan had been dropped once during the five-ODI series and Kohli had opened the innings. Such a move is unfathomable now, but with scores of 12, 0, 32, 12, 28, 9 and 11 (7 innings in South Africa, New Zealand and England) in conditions that will be similar to the World Cup, the attacking opener is not doing himself any favours.
For once, India's bowling attack isn't a cause for concern. However it will be interesting to watch how the bowlers will cope if they are met with an unhelpful track at Trent Bridge.
Teams: India: MS Dhoni (c & wk), Shikhar Dhawan, Rohit Sharma, Virat Kohli, Ajinkya Rahane, Suresh Raina, Ambati Rayudu, Stuart Binny, Sanju Samson, R Ashwin, Ravindra Jadeja, Karn Sharma, Mohit Sharma, Umesh Yadav, Mohammad Shami, Dhawal Kulkarni, Bhuvneshwar Kumar.
England: Alastair Cook (c), Moeen Ali, James Anderson, Gary Ballance, Ian Bell, Jos Buttler (wk), Steven Finn, Harry Gurney, Alex Hales, Chris Jordan, Eoin Morgan, Joe Root, Ben Stokes, James Tredwell, Chris Woakes.
Match starts at 3 pm (IST).