Brown joined the Skrill Premier club in October on an initial one-month deal which expired after the Sandgrounders' 5-1 league defeat at Aldershot on Saturday.
The 23-year-old summer signing has yet to feature for the Spireites since joining the club from non-league Marine.
He scored on his Southport debut this month as Alan Wright's men became the first team to defeat league leaders Cambridge, beating the U's 1-0 on November 2.
Brown has made five appearances for Southport but came off at half-time during their loss at Aldershot on Saturday with a tight hamstring and he is not expected to be fit in time for their trip to Luton on Tuesday night.
- Sports & Recreation