The 24-year-old spent six years at Dagenham & Redbridge before moving to London Road last season.
Griffiths told the club website: "I am delighted to be staying a couple more months as I am enjoying my football and am pleased we have started so well."
Manager John Sheridan added: " We are pleased to keep him, he has done really well.
"I think the Chesterfield fans have been quite impressed by what they have seen of him."
The Spireites are fourth in League Two and remain unbeaten after four games.
Source: BBC Sport
Source: BBC Sport