The pair were due to face Xu Si and Jak Jones respectively on the opening day of competition on Monday, with Xu and Jones now advanced to round two.
Hamilton, who suffers from asthma, controversially withdrew from the World Championship at the Crucible in July citing fears over plans to admit a limited number of spectators.
Ryan Day & Anthony Hamilton have tested positive for Covid-19 at the @betway UK Championship.
— World Snooker Tour (@WeAreWST) November 23, 2020
The four-time Crucible quarter-finalist said at the time: “On a personal front I’m high risk – I’ve got asthma so I’ve been diligent to say the least during this lockdown.”
However, Hamilton has played in subsequent tournaments, including losing in the first round of last week’s Northern Ireland Open at the same venue.
World Snooker said in a statement: “All other players and officials tested at the event so far have had negative results.
“Hamilton and Day will now undergo a period of self isolation and will receive the support of WST.”