Howard, 25, died in hospital Sunday, according to a statement from Durham City Rugby and Football Club (DCRFC) and the UK Foreign Office.
British rugby is in shock following the death of a club player while touring Sri Lanka.
The membership confirmed with "nice disappointment" that Baty, his 26-year-old teammate had additionally died Tuesday.
A British amateur rugby player has died and another is critically ill after complaining of breathing difficulties on returning from a nightclub in Sri Lanka.
In a statement released on Tuesday, the club requested that the privacy of their families would be 'respected and upheld at this hard time'.
The pair had visited a nightclub within the Sri Lankan capital Saturday throughout a tour of the nation with their crew Clems Pirates RFC.
Durham City Rugby Club, which oversees the team, said in a statement the pair suffered "non-rugby related breathing problems".More news: Drake returning to Xcel Center Aug. 1 with 'Three Amigos' in tow
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The following morning, two players fell ill and were taken to hospital, police said.
The two players complained of breathing difficulties to the hotel management at about 10:00 on Sunday.
"The club requests that the Howard and Baty families' right to privacy is respected and upheld at this most hard time".
The visiting team played against CR&FC on Saturday (12) and it was reported that the match ended with no evident injuries to players from any of the teams.
Durham City RFC president Richard Wilkinson said: "Both players and Clems Pirates hold a special place in our rugby family, and our continued support is unconditional".
"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.