The tungsten is required to meet minimum weight requirements on the car and the NASCAR rule book states if it is separated at any point it is an automatic four-race suspension for the crew chief, car chief and engineer.
Chris Gabehart, the crew chief, was suspended along with car chief Brandon Griffeth and engineer Scott Simmons.
Sam McAulay will be the crew chief, while Eric Phillips will be car chief and Scott Eldridge the engineer.
NASCAR's next four races are at Charlotte, Bristol, Atlanta and Martinsville between Wednesday night and June 10, when the suspension ends.
Hamlin won not only the season-opening Daytona 500 but also won last Wednesday night at Darlington Raceway.