Griffin sustained the concussion during Sunday's game against the Atlanta Falcons on a hit to the head by Falcons linebacker Sean Weatherspoon.
He was taken out of the game at that point, but on Monday showed no signs of post-concussion symptoms, the coach said.
Griffin was experiencing "no dizziness, no headaches, and no vomiting," Shanahan told reporters.
"We're going to go through the process with Robert, hopefully there is no setback and he's ready to go" for the Redskins' next game against Minnesota, he added.
Swim Week Miami Beach 2014 [PHOTOS]