The injury occurred Saturday when Guyer went after a foul ball in Houston.
"When he went into the stands, he got like a forearm or something,'' manager Terry Francona said. "We checked him for concussions, but his neck is whiplash-ish kind of, so he hasn't played since that. I think he could've if he had to, but we're trying to be mindful of it. On the 10-day DL, we can backdate it a couple days, so it should work out OK.''
Guyer is batting .150 with three homers and 10 RBIs in 33 games. He becomes the fourth outfielder on Cleveland's DL, joining Bradley Zimmer (left rib contusion), Tyler Naquin (left hamstring strain) and Lonnie Chisenhall (right calf strain).
The move is retroactive to Sunday.
Plutko is replacing Josh Tomlin in Cleveland's rotation. The 26-year-old Plutko made his season debut with the Indians on May 3, pitching 7 1/3 innings in the second game of a doubleheader against Toronto and earning his first major league win.