The left-hander appeared in two games from the bullpen at Class A Peoria earlier this season before being sent to Extended Spring Training in Arizona.
While there, Pawelek spent a good amount of time working on mechanics.
Then, as he was set to leave Mesa for the start of short-season play in June, the 20-year-old southpaw suffered a freak accident resulting in the injury.
His elbow did not require surgery, and after remaining in Mesa for nearly six weeks of rehab, Pawelek said Tuesday morning that he is ready to go.
"I got cleared last Friday, went out and pitched an inning (on Saturday), and then they said I was going to Boise," Pawelek said.
"I'm headed up there right now actually."
It is not yet clear if Pawelek will return to starting immediately or if he will briefly pitch from the bullpen. His outing on Saturday was in relief, where he faced six batters and yielded one unearned run on two hits.
But Cubs Director of Player Development Oneri Fleita indicated that Pawelek could return to the starting rotation right away.
"He should not be very far away from going out and giving us quite a few (innings) when he goes out his first time," Fleita said.
"He should be able to go right into a game, and his pitch count should be built up pretty good because our guys have done a good job having him throw in some simulated games behind the net to protect his arm."
Pawelek spent last season in Boise, where he was 3-5 with a 2.51 ERA, making 12 starts and logging 61 innings. He struck out 52 and walked 23.
"I only threw one inning (in Mesa), but I threw a lot of flat-ground work and bullpen work to make sure I could throw strikes," Pawelek said of his recent work in Arizona before adding, "I'm happy to get out of here."