Several groups have called for Goodell to resign after a report emerged that the league had a copy of a video, which showed Rice striking his wife, in their possession for three months before its release on Monday.
However, Snyder is the latest NFL owner to back the commissioner, and he has insisted that Goodell has to remain in his position.
"Roger Goodell has always had the best interests of football at heart, both on and off the field," Snyder said in a statement.
"We are fortunate to have him as our commissioner. The entire Washington Redskins organisation strongly endorses his efforts to eradicate domestic abuse and the independent investigation into the Ray Rice assault."
The NFL has hired an independent investigator to examine their handling of the Rice assault case.