Although no timetable has been announced, the initial belief is that Niemann, who was put in a walking boot and on crutches, will be out four to six weeks.
With two on and one out, Lind hit a line drive off the right leg of Niemann, who then recovered and threw Lind out at first. Niemann made it through the rest of the inning, but was pulled before the start of the second and replaced by left-hander Cesar Ramos.
"It's a tough break, literally," Rays manager Joe Maddon said. "The ball was not hit that sharply, so I thought it would just be like a stinger and he'd be able to walk it off. I was watching him go out to the mound and I didn't like the way he was walking. He just did not have a good look about him at all. It's an unfortunate thing; we've had our share already. It's not easy to lose a pitcher of his caliber."
Niemann, 29, is 2-3 with a 3.38 ERA over seven starts. In a season where the Rays have been hit hard with injuries, it was difficult for his teammates to learn of the news and see another player land on the disabled list.
"It's tough, a lot of adversity right now," Ben Zobrist said. "We're just trying to keep nine bodies on the field. Luckily, we have a lot of capable guys on the bench and in the organization that can come in and help the team out. We've faced adversity in the past and done fine through it, so hopefully guys can pick up the slack."
Outfielder Desmond Jennings was placed on the 15-day DL before Monday's contest, joining a long list of Rays players who are out, including All-Star third baseman Evan Longoria.
No decision on Niemann's replacement has been made. Wade Davis is a candidate, but Maddon likes the way he has pitched out of the bullpen. If Davis is left in the 'pen, the Rays could call upon Minor Leaguers Alex Cobb or Chris Archer.
Chris Toman is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.