Police say a post-mortem has yet to be conducted.
"Subsequently, one of the two has died and one remains in hospital", the statement said.
He and teammate Thomas Howard, aged 26, suffered breathing difficulties on Sunday and Howard died shortly after being admitted to hospital.
The pair were both admitted to hospital in the city of Colombo on Sunday.
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A photo issued by Durham City Rugby Football Club of amateur player Tom Baty.
The death was confirmed to News 1st, by Police Media Spokesperson SP Ruwan Gunasekara.
'Both players and Clems Pirates hold a special place in our rugby family, and our continued support is unconditional'.
A club statement released on Durham City RFC's website said: "It is with great sadness that the club can now confirm that Tom Baty, 26, from Durham City has died this afternoon following his admission to hospital on Sunday, 13 May".
Durham County Councillor David Boyes said Durham City RFC was a very well organised, well equipped organisation and oversaw a number of teams.
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The club previously said that in both cases the breathing problems were non-rugby related.
Durham County Councillor Richard Ormerod said it was very sad news for all those involved.
The British High Commission (embassy) in Colombo said it was supporting the families of the two victims and were in contact with the local authorities.
He added that Clems Pirates was well known in the community.
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