Dahl was scratched from the lineup last week with what the Rockies initially described as back soreness and was expected to miss a few days.
Black told reporters Monday that Dahl, 22, could possibly return to play in games before the end of spring training.
"Extended [absence] is, to me, like months -- this is not," Black said, according to MLB.com. "Baseball activity hopefully will start in a couple weeks. ... I do anticipate him getting into a game here. If not, then it doesn't happen."
Dahl is battling with veteran Gerardo Parra for the Rockies' starting job in left field this spring training.
Dahl was selected with the 10th overall pick in the 2012 draft and enjoyed a solid start to his major league career last season, batting .315 with seven home runs in his first 63 games with the Rockies.