O'Donnell joined Stockport in the middle of last month in order to play some regular first-team football after losing his place in goal to Tommy Lee.
The 24-year-old keeper made his debut for the Blue Square Premier side in a 3-1 defeat against Mansfield and then played in a 2-1 victory over Forest Green
He has been unable to make any further appearances due to several fixtures being postponed because of the weather.
There is a recall clause in the deal, allowing manager Paul Cook to bring him back to the Proact with 24 hours notice if required.
O'Donnell, who joined the Spireites last summer after being released by Sheffield Wednesday, made his debut as a substitute as a replacement for the injured Lee in the Johnstone's Paint Trophy tie at home to Oldham in early September. He then appeared in the next 15 games before losing his place when Lee regained full fitness in November.