Baez batted .260 with 23 home runs and 80 RBIs in 104 games at Triple-A Iowa. The 21-year-old hit .300 with 12 homers and 34 RBIs in his last 32 games there, including a two-homer performance Sunday.
Iowa manager Marty Pevey called Baez, who hit a two-run homer in the All-Star Futures game last month, to his hotel room early Monday to give him the news.
"He was half asleep," Pevey told MLB's official website.
The arrival of Baez will likely push Alcantara to the outfield, with the 2011 ninth overall pick taking over at second base and batting second Tuesday. Baez had been batting third in Triple-A, followed by Cubs No. 1 prospect Kris Bryant and recently another top prospect, Jorge Soler.
"He has the ability, he has the talent," shortstop Starlin Castro said. "I think he can do the same - come here and keep playing, keep doing his job. I think it'll be good for him."
Baez will try to help his new team avoid its 13th loss in 15 games in Colorado, where the Cubs haven't won a series since August 2004.
Colorado's Troy Tulowitzki is hitting .415 with 14 RBIs in his last 10 home games against Chicago, but the All-Star shortstop is on the disabled list with a left hip flexor strain.
Teammate Carlos Gonzalez has batted .465 with three home runs in 12 career home games against the Cubs. Manager Walt Weiss said he's confident the outfielder will be back in this series after missing the last two contests due to an ankle injury.
Gonzalez, however, is hitting .143 in his last 23 games, including 1 for 14 last week when Colorado dropped three of four at Wrigley Field, and is 0 for 10 lifetime against Cubs starter Travis Wood (7-9, 5.10 ERA).
The Rockies (44-67), the only NL team with a worse record than Chicago (47-63), hope to avoid their eighth loss in nine games after getting swept in Detroit over the weekend. They managed only four hits Sunday in a 4-0 defeat.
"Good things are bound to happen," outfielder Brandon Barnes told MLB's official website. "We've had some setbacks, some injuries, but at the same time, we need to go out there and battle every single day."
Colorado has averaged 2.8 runs during a 2-18 road stretch but has scored 6.8 per game in winning three of four at Coors and is batting a major league-best .316 at home.
Brett Anderson (1-3, 3.12) helped the Rockies to their only win in Chicago last week when he allowed two runs despite giving up a season-high 11 hits over seven innings in Wednesday's 6-4, 10-inning victory.
The left-hander is 1-0 with a 1.33 ERA in his last three outings.
Wood opposed Anderson last week, allowing four runs with a season-high 11 strikeouts over six innings.
The left-hander has gone 0-4 with a 6.33 ERA in eight starts since winning June 15 at Philadelphia. He's particularly struggled on the road, going 4-6 with an NL-worst 6.27 ERA in 11 starts.
Wood is 1-1 with a 2.77 ERA in five outings - four starts - against Colorado, but hasn't started at Coors since 2010.
The Cubs seek their sixth win in eight games after taking two of three at Dodger Stadium.
Chris Coghlan had a home run and a double in Sunday's 7-3 win, leaving him 11 for 23 over his last six games.
Castro, who went 7 for 12 with three RBIs in the series, is hitting .424 in his last eight contests at Colorado. Fellow All-Star Anthony Rizzo is batting .364 over an eight-game hit streak against the Rockies.