Heyward injured a knuckle on his right hand while diving for a ball in the outfield on Friday. He will be eligible to come off the disabled list on May 16.
Heyward was off to a decent start in 2017, after having a year to forget last season. He was hitting .253 this season, with three home runs and a .333 on-base percentage, before going down with the knuckle injury. He also was playing stellar in right field.
Heyward injured his wrist last year, and adjustments to his mechanics led to his worst campaign at the plate. He hit a career-low .230, with just seven home runs.
The Cubs' bullpen could use some relief, especially after Sunday night's marathon against the Yankees.
Even after his wrist healed, Heyward never found his groove; he reworked his swing during the winter.
The Cubs want him fully healed before he returns.
Floro, 26, came up in the Tampa Bay Rays organization and made his major league debut last season. This year, he was 1-0 with a 5.06 ERA in eight appearances for Triple-A Iowa.
The Cubs have a need for extra arms after playing an 18-inning game on Sunday night, a day after starter Brett Anderson recorded only one out before leaving an outing with back tightness. The Cubs now have nine relievers as they open a series against the Colorado Rockies.
The Cubs also traded outfielder Matt Szczur to the San Diego Padres on Monday for minor league righty Justin Hancock, who was drafted by Chicago general manager Jed Hoyer in 2011 when Hoyer held that same position with the Padres. Hancock, 26, has a career 3.91 ERA in seven minor league seasons. He has appeared in 116 games, starting 90 of them.