Waltrip's No. 55 Toyota was cited after last Sunday's Gatorade Duel qualifying runs.
NASCAR officials said there were three serious violations, including illegal car parts components and a gasoline additive.
Hyder has been suspended indefinitely.
Reports have said an unspecified substance was found in the intake manifold.
"I am ready to bear all responsibility for what happened," Waltrip said. "I am here today to apologize to the NASCAR fans, sponsors and other team owners. You can't hurt me any worse than I am right now. We haven't fired anyone nor do we plan on firing anyone until we know what happened. We are aggressively trying to find out what happened. What took place was the act of an individual or individuals and is not a reflection on our team."