The 27-year-old signed an initial short-term deal with the Latics last month after impressing in a trial spell with the club and has made two first-team appearances for John Sheridan's side to date.
He came on as a substitute in the 3-3 draw at Hartlepool United before making his first start in the 3-1 defeat at Stockport County.
Byrne left Pittodrie in the summer after making 59 appearances for the Dons.
He teamed up with Oldham after failing to impress during trials with Wigan Athletic, Paris St Germain and NEC Nijmegen.