Rogers, 9-3 with an American League-leading 2.46 ERA, broke a bone at the base of his right pinkie after coming out of his last home start, June 17 against Washington, manager Buck Showalter said Monday.
"It's an emotional game ... most of the time you don't break a small bone," Showalter said after pointing out a cooler at the end of the dugout. "The good news, it's nothing serious enough to keep him out over an extended period of time."
Showalter said the left-hander will miss his scheduled start Tuesday against the Angels, and indicated Rogers could miss another turn as well because it would take 10 to 12 days for the broken bone to heal completely.
The Rangers, however, didn't put Rogers on the disabled list to make room for catcher Gerald Laird, who was recalled Monday from Triple-A Oklahoma and started against the Angels instead of Rod Barajas (strained back muscle). Infielder Marshall McDougall was optioned to Oklahoma.
After a 13-3 loss in which the Rangers used four pitchers, Showalter said the disabled list was still a possibility for Rogers.
"We'll talk more [Tuesday]. We'll decide if we need another pitcher," Showalter said. "We trusted Kenny and we talked to him about a lot of things."
John Wasdin (0-0, 1.38 ERA in five relief appearances) will start in Rogers' place Tuesday night.
Rogers gave up six runs, 10 hits and three walks in 3 1/3 innings of a 6-0 loss last Wednesday at the Angels. He won his previous nine decisions, a career best, including the game after which he got hurt.
"He wanted to pitch with it and felt like it wouldn't be a problem," Showalter said. "How much it had an effect on his last start, obviously it was a break from what he was doing."
Rogers refused to talk to reporters in the clubhouse after Monday night's game. The 40-year-old left-hander has boycotted most media since a report before spring training that he threatened to retire if he wasn't given a contract extension.
Against Washington, Rogers allowed 12 baserunners in 6 1/3 innings -- but only one scored.
Rogers was visibly upset when umpires ruled that the final Nationals hitter he faced checked his swing on a full-count pitch. Rogers spiked the ball to the ground when Showalter came out to remove him from the game and found the cooler soon after that.
The Yankees' Kevin Brown broke his left hand when he punched a clubhouse wall in frustration last Sept. 3. The right-hander needed surgery and didn't pitch again until Sept. 26.