The NHL's Department of Player Safety announced the suspension Thursday after holding a hearing with Killorn.
Nelson chipped the puck out of his own zone during the first period of Game 2, an eventual 2-1 Tampa Bay win.
"Well after Nelson releases the puck, Killorn approaches from behind and, having seen nothing but Nelson's numbers for some time, delivers a forceful check to the defenseless Nelson, driving him dangerously into the boards," says a narrated video, released by the DOPS to explain the ruling.
Killorn was issued a major penalty and game misconduct for the play. Nelson also left to receive medical attention but returned after clearing concussion protocol.
Nelson also took an unpenalized cross check from Tampa Bay's Barclay Goodrow in the second period. Islanders coach Barry Trotz said he believed the second hit "was a little bit of a target to the head. They knew he was hurt, they targeted it a bit."
"I felt like I was getting hit quite a bit," Nelson said after. "You fight through it and get to your game."
The Lightning lead the series 2-0.
Killorn doesn't have a lengthy history with the DOPS, having been fined only once during his 585-game NHL career. Earlier Thursday, Tampa Bay coach Jon Cooper said he would be "mildly surprised" if Killorn wasn't available for Game 3.
The Lightning, who have been dressing only 11 forwards and seven defensemen, might be down another forward for Game 3 as well. Leading scorer Brayden Point was injured during the second period of Wednesday's game and did not return. Cooper did not yet have an update on Point on Thursday.