Team owner Dietrich Mateschitz also was docked 150 owner points, while Hamlin and car chief Craig Smokstad were both suspended indefinitely.
Red Bull Racing general manager Jay Frye said the team accepted responsibility and would not appeal the penalties.
The infraction was discovered after the No. 83 Toyota was randomly selected for a post-race inspection following Vickers' 11th-place finish at Martinsville Speedway. The car was sent back to NASCAR's R&D Center in Concord, where it was discovered the sheet metal did not meet minimum thickness requirements.
"This approach to racing is against the values of the Red Bull Racing Team, and the necessary steps will be taken to rectify the situation ensuring it does not happen again," Frye said. "It is a privilege to race in the NASCAR Sprint Cup Series, and we are taking this penalty seriously."
Frye said Randy Cox, manager for Red Bull's research and development program, will replace Hamlin at this weekend's race in Atlanta.
There are just four races left in the season, and typical crew chief suspensions have been for six weeks. It was not clear if Hamlin and Smokstad's suspensions will carry over into 2009 and the season-opening Daytona 500.
Vickers is tied for a career-best 15th in the standings, but the penalty drops him to 17th. Without Hamlin, who took over the No. 83 at the start of the year, it will be difficult for Vickers to better his 2006 final points standings. Vickers was in his final year with Hendrick Motorsports that season and earned the only Sprint Cup Series win of his career with a victory at Talladega.
He moved to Red Bull in 2007, and both he and the team struggled in their inaugural season. The No. 83 team failed to qualify for 13 races, and Vickers finished 38th in the final standings.
It meant Vickers had to qualify on speed for the first five races of the year, until he could crack the coveted top-35 mark that guarantees a team a spot in the starting field. He easily made it, and Red Bull has since set its sights on scoring its first Sprint Cup victory.