The 65-year-old Cronberg recently announced plans to step down as chair of the Green League, which she has led since 2005. The party is to elect her successor in mid-May.
She said on Thursday that she has begun treatment, which will be continued this spring as needed.
Cronberg says she plans to handle her ministerial duties as usual for now, taking medical leave if needed.
Cronberg, who holds two doctoral degrees and is the former director of the Copenhagen Peace Research Institute, lives in North Karelia. She was chosen as Labour Minister nearly two years ago despite narrowly losing a bid for re-election to Parliament that spring.
The party will become the first to choose a leader through direct election by all members. So far the only announced candidate to succeed her is MP Anni Sinnemäki, head of the party's parliamentary delegation. Four years ago Sinnemäki sought the job, but lost to Cronberg. MP Ville Niinistö is considering a run for the post.
The Greens are Finland's fourth-largest party, with support rated at 10.2 percent by a YLE poll released in early February.