The activists said they wanted to demonstrate what they considered inadequate security at the facilities, the Swedish news agency TT reported.
Greenpeace said the action was a "peaceful stress-test" of security at plants at Forsmark on the east coast and Ringhals in the south.
Local police said nine activists breached the first barrier at the Forsmark plant and climbed light posts. Greenpeace said 50 activists entered the restricted areas.
Some 20 activists entered the Ringhals plant on bicycles. It is unclear how they entered the gate, which is manned.
Police said 43 people were arrested at Forsmark and 16 at Ringhals.
Annika Jacobsson, head of Greenpeace Sweden, said the breaches showed that security at the plants was "alarmingly lax."
While activists have previously entered the plants' grounds, officials say no one has ever gotten close the reactors.
Greenpeace argues that no one should be able to gain entry at all, and that security is so inadequate the plants should be shut down.