The defender went to ground clutching his left leg after pulling up in the 66th minute of the 3-0 loss on Saturday.
It is feared Robertson will miss the club`s remaining five matches this season as the runaway league leaders close in on the League Two title.
"It looks like he has ruptured the Achilles. We will take him to visit our specialist this week for a confirmed diagnosis," said Chesterfield physio Jamie Hewitt.
Source: PA
Source: PA