19-year-old Picken, who can operate at right-back or in midfield, will be in the Spireites' squad for Saturday's League One game at Oldham.
"We are pleased that Phil is joining us as he will give our injury-hit squad a welcome boost," said assistant boss Lee Richardson.
Chesterfield-born talent Hurst can also play up front. The 19-year-old has had spells at Boston United and Stockport.
Richardson added: "As a Chesterfield lad he will want to give it that bit extra for his home team and should do well."