During practice Wednesday, Andersen kicked about 10 balls, then retreated inside to ice his tender knee.
Giants Head Coach Jim Fassel said that Andersen "may have overdone it a little bit."
The Giants may very well head into their season opener with rookie Owen Pochman handling both the kickoff and field-goal kicking duties. Pochman, a seventh-round pick of the Patriots, was signed earlier this week as insurance against Andersen's injured knee.
Also, on Wednesday, WR Ike Hilliard practiced for the first time since having toe surgery in June. He ran several routes, and looked good in the process.
"To me he looked better than I thought he would," Fassel said. "He actually ran and looked pretty smooth."
Hilliard was listed as questionable, but certainly shouldn't be ruled out for the Denver game.
In addition to Andersen, four other players were listed as probable for the Broncos game. WR Joe Jurevicius (concussion) and TE Howard Cross (knee) practiced while DT Cornelius Griffin (ankle) and CB Jason Sehorn (knee) sat out.