The Raiders also placed running back Kenyan Drake on the non-football injury list.
Richard, who has openly questioned and sometimes condemned the use of vaccinations over the past few years on his social media accounts, and Riddick were the only two players on the Raiders' camp roster to not be seen during practice.
A day earlier, Raiders coach Jon Gruden said the team was fully vaccinated, "with the exception of four or five" players.
Early Wednesday, quarterback Derek Carr hinted he had taken the vaccine and said the choice to be vaccinated or unvaccinated remained up to the players themselves.
"I've been getting shots since I was a little kid," Carr said. "I've had my mom take me out of school, 'Hey, we've got to go get this shot.' I remember that as a kid. My kids, too. This one, it's a little different because it's new, right? The other ones -- with measles, mumps, Hepatitis B, all that kind of stuff -- this one is new. So people and families have certain opinions.
"And if someone wants to ask me my opinion, absolutely, I'm sharing my opinion. Absolutely. But if they don't want my opinion, I don't think it's my right to go tell them what to do, as a man. Especially in America. I don't think it's my right to do that. If they want my opinion, I will absolutely give it, 100 percent. No problem with that. But I think it's up to them and their family because they know what they want to do for their family. I can't make the decisions for them and their kids and stuff."