His teammate Thomas Howard, 25, died at around noon on Sunday, shortly after the pair were admitted to hospital with breathing difficulties.
Both from Durham, the players were on tour with one of the club's teams called the Clems Pirates.
They were admitted to hospital after they started suffering from breathing problems.
Clem Pirates were in Colombo on tour, having arrived last Wednesday, before facing Ceylonese Rugby and Football Club (CR & FC).
A statement on the Durham City Rugby Club 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, May 13".
The Foreign Office confirmed it was dealing with the incident: "Our staff are supporting the family of a British man following his death in Sri Lanka, and are in contact with the Sri Lankan hospital services".
A British Rugby player dies in Sri Lanka Mon, May 14, 2018, 11:23 am SL Time, ColomboPage News Desk, Sri Lanka.
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The club previously said that in both cases the breathing problems were non-rugby related.
"We ask the media to respect the privacy of the families at this very hard time".
The following morning, two players fell ill and were taken to hospital, police said.
After the match, they had visited the club and team members returned to their hotel in smaller groups by early Sunday.
The two players complained of breathing difficulties to the hotel management at about 10:00 on Sunday.
"We are assisting the family of a British man who has been hospitalised in Sri Lanka, and are in contact with the Sri Lankan medical services", it added.