The hard-throwing Alcantara went 7-5 with a 4.31 ERA in 25 games (22 starts) with Springfield and had 106 strikeouts with 54 walks in 125 1/3 innings.
Matheny said the plan is to use Alcantara as a reliever for now.
"Pitch him and see how it looks," Matheny said. "We have a bullpen with a lot of openings and opportunities. And give him a chance to show what he can do."
• Cardinals' Top 30 prospects
Alcantara held opponents to a .262 average this season while relying primarily on a fastball that routinely clocked between 94-96 mph. That velocity, coupled with a hard curve and solid changeup, have the Cardinals salivating about Alcantara's prospects.
"There's always excitement that come with that," Matheny said. "Sometimes that velocity certainly can create some room for error. The ball jumps out of his hand and makes guys have to cheat a little bit. He's got really good command too of his secondary pitches so I think that's going to be the difference-maker whether or not he can control the strike zone with his fastball and still use those other pitches effectively."
Matheny acknowledged that Alcantara is far from a polished product but said the 6-foot-4, 170-pounder will have to learn on the fly now that he's in the Majors.
"He's going to have to figure the developing stuff as he goes," Matheny said. "He'll be developing while he's getting the opportunities. He's developing as much as he can be a guy that can get us the outs that we need at any particular time, whether they're games that are lopsided one way or the other, which typically that's how the young guys get their chance, or if we got pitchers that are down. That's how they get their chance and then develops into more, bigger opportunities."
The Cardinals also called up catcher Alberto Rosario from Triple-A Memphis and recalled infielder Alex Mejia and outfielder Harrison Bader. Bader is the No. 5 prospect in the system.
Pham out of lineup
Outfielder Tommy Pham was not in the starting lineup Friday after jamming his thumb sliding into a base on Thursday.
Michael Wagaman is a contributor to MLB.com. He covered the Cardinals on Friday. This story was not subject to the approval of Major League Baseball or its clubs.