Arrieta has been plagued by a cut on his right thumb that impacted his last start while Hoerner injured his left forearm colliding with center fielder Ian Happ as the two converged on a ball in Sunday's game against the Cincinnati Reds. Winkler has right triceps tendinitis.
"We're optimistic about everyone, to be honest with you," Cubs manager David Ross said. "I don't think they are very serious. I think all of them are fairly good news with the off days coming up for us. It gives a chance to maximize the rest time without missing too many games."
Happ is also hurting from the collision with Hoerner. Ross listed him as day-to-day with soreness in his ribs after he was kicked going to the ground for the popup.
Arrieta, Hoerner and Winkler were all having productive starts to their season before going down with their injuries. Taking their place on the roster, the team recalled lefty Kyle Ryan, righty Keegan Thompson and infielder Ildemaro Vargas.