Burgess, on loan at League One club Bury from Fulham, earned his spot after helping his side to a 1-0 win at Charlton Athletic over the weekend.
The EFL Team of the Week is made up of the best players from the Championship, League One and League Two in England.
Burgess was a rock for the Shakers, standing firm against a late onslaught from Charlton at the Valley.
His selection is a reward for a superb run of form for the 21-year-old since joining Bury in January.
Bury has lost just one of eight matches since Burgess has been in the side, keeping three clean sheets in the process.
The upturn in results has helped the Shakers pull away from the relegation zone in League One, currently 19th and three points above the drop zone.
They take on fellow strugglers Coventry in a crucial match on Wednesday (AEDT), where Burgess will come up against fellow Aussie Andy Rose.
Source : Football Federation Australia