Spencer has practiced one time this summer, the first practice of training camp, until he experienced knee issues. Spencer underwent surgery on July 25, and it was thought he would miss two to four weeks.
But Spencer said he suffered a setback on Monday when he noted his knee developed some swelling.
George Selive, who was signed the day Spencer had surgery, will start at end in his place.
Also, the Cowboys made newly signed guard Brian Waters inactive. He was signed officially on Wednesday and has practiced just three times.
Waters, who hasn't played since 2011, is still working on his conditioning.
Giants inactives are quarterback Ryan Nassib, center David Baas, tackle David Diehl, tight end Adrien Robinson, defensive tackle Johnathan Hankins, defensive end Damontre Moore and defensive end Adewale Ojomo.