But the Pirates will need a longer-term replacement for the ace right-hander, who revealed that his "right calf strain" is actually a Grade 1 tear in the calf.
"I tried to give it a day, but it was the same. I can barely put any pressure on it," said Burnett, who was dragging his right foot around in a heavy walking boot and said he incurred the injury during his normal running program on Wednesday.
"I kind of wish I'd done it goofing off," he said, "but I was just doing my normal running. I went to slow down and decelerate and felt a pop. It was a cramp at first; I felt something and it cramped up.
"I'm treating it all day, just got to stay off it. Hopefully I can get back sooner than later and not have this turn into a six-week thing, take my time and keep it a two-week thing."
Cumpton, 24, arrives with promise, but has no promises. The Pirates' ninth-round pick in the 2010 First-Year Player Draft began this season with Double-A Altoona but earned a quick promotion to Indianapolis, where the right-hander had an ERA of 3.31 in 11 appearances (10 starts).
"[Cumpton is] a three-pitch guy, a strike-thrower to both sides of the plate. He's a competitor," said manager Clint Hurdle, preferring to not project beyond Saturday's start. "No need to get ahead of ourselves. We'll give him the ball and see where he can take it. We'll take it one start at a time."
Cumpton got word of the callup Thursday night while the Indians were on the road to face Durham and said he "was shocked. I didn't see it coming. I was blindsided."
Tom Singer is a reporter for MLB.com and writes an MLBlog Change for a Nickel. He can also be found on Twitter @Tom_Singer. This story was not subject to the approval of Major League Baseball or its clubs.