Ms Burgess took up the role just six months ago and was set to continue for another year, but her term was cut short on Sunday when the Shrewsbury Town Council results were announced.
She was beaten by the Liberal Democrat challenger in her ward of Meole, mirroring the Shropshire Council result the previous day.
It was one of four losses for her party in the town council poll, as the Lib Dems also took Bowbrook and Copthorne – unseating Shropshire Council leader Peter Nutting in the process.
Meanwhile the Greens took Radbrook, with Chris Lemon winning a second seat for the party on the town council.
The premature departure of Ms Burgess means deputy mayor Julian Dean, who was re-elected in Porthill for the Greens, is expected to step up to the top job – subject to a vote at the first meeting of the new council.
Labour remains the biggest town council group with seven members, and the Liberal Democrats are now the second party with six.
Town council leader Alan Mosley retained his Castlefields and Ditherington seat for Labour as did councillors Kate Halliday (Belle Vue), Kevin Pardy (Sundorne), Pam Moseley (Monkmoor), and Phil Gillam (Sutton and Reabrook).
They are joined by two new Labour members – Rosemary Dartnall in Column and Elisabeth Roberts in Harlescott. Both seats were won by Labour in 2017 but have been independent since 2019 after the previous councillors left the party.
Councillor Mosley said he hoped to carry on as town council leader.
He said: “It will clearly be interesting to see how things change on the town council.
“We hope that we will be able to continue with improvements and progress even more quickly, and to greater effect, than in the past.”
Liberal Democrat group leader David Vasmer retained his Underdale seat, and Nat Green was re-elected in Quarry and Coton Hill.
They are joined by new Lib Dem councillors Mary Davies, who takes over from Hannah Fraser to represent Abbey, and Alex Wagner (Bowbrook), Rob Wilson (Copthorne) and Bernie Bentick (Meole), who all took Conservative seats.
Completing the line-up, Conservative group leader Alex Phillips was re-eleced in Bagley, as was Becky Wall in Battlefield.