The roster moves mark the first coronavirus-related issues ahead of Sunday's Super Bowl.
"The NFL has done a great job with it, presenting different safety things for the players to stay as safe as possible," said Chiefs coach Andy Reid, who noted that he was first notified of the situation Sunday. "We've been hammering this point home forever. The problem is you're fighting the invisible man. It just gets you when least expected, and we're seeing that in everything. It's an unfortunate thing."
Robinson, 26, had a career-high 45 receptions for 466 yards and three touchdowns this season.
Kilgore, 33, appeared in seven games -- including four starts -- this season, his first with the Chiefs. The 10-year veteran is listed as Kansas City's backup center behind Austin Reiter.
"These guys were being as safe as they could be," Reid said, "and we'll just see how it goes. But the league has built-in rules and regulations, so we follow those, and it'll all work out. It'll all work out for them when it's all said and done."
Information from The Associated Press was used in this report.