Barkley (ankle) was listed as a non-participant on Monday's estimated injury report, Dan Salomone of the Giants' official site reports.
Barkley injured his right ankle in the waning minutes of Sunday's eventual 31-28 win at Arizona, needing assistance to get to the sideline and walking with a visible limp. An X-ray after the contest was returned negative, but an MRI on Monday revealed an "ordinary" sprain that may sideline him for around three weeks, per Jordan Raanan of ESPN.com. As it stands, Barkley isn't expected to suit up for Thursday's game in San Francisco, which would leave Matt Breida to lead the Giants backfield. Behind Breida, Gary Brightwell, Eric Gray and practice-squad member Taiwan Jones are the team's other options at running back.