Reed appeared to roll his ankle during the first quarter but returned in the second. The 49ers later ruled the tight end out after the television broadcast showed the team's medical staff examining Reed's left knee and leg.
Shanahan said Reed indeed sustained ankle and knee injuries.
Cornerback Emmanuel Moseley was ruled out with a concussion after a collision in the second quarter with safety Jaquiski Tartt as the two defenders attempted to tackle Giants quarterback Daniel Jones.
Other injuries from the game include running back Jerick McKinnon, who suffered an upper rib injury in the fourth quarter. Shanahan also noted that linebacker Mark Nzeocha suffered a quad injury.
The 49ers will return to the West Coast to begin preparing for their Week 4 matchup against the Philadelphia Eagles.