The United Nations said two soldiers had been reported killed, apparently during the same firefight that led to the abduction.
"Initial indications suggest that a soldier has been abducted," spokesman Lieutenant Colonel Peter Lerner told journalists.
Asked if that meant the truce was over he replied: "Yes. We are continuing our activities on the ground."
Hamas, the main political and military power in Gaza, neither confirmed nor denied the capture.
But it said Israel's announcement of the capture was simply a "justification for Israel retreating from the truce, and a cover-up for massacres especially in Rafah," referring to Israeli shelling that killed at least 40 people just hours after the truce took hold.
Lerner said the soldier went missing during a clash with fighters who emerged from a concealed tunnel.
He said the clash took place in Rafah, on the border with Egypt, where an AFP correspondent earlier reported fierce fighting as the army warned residents to stay in their houses.
A separate military statement said the incident took place at around 0630 GMT, 90 minutes after a 72-hour ceasefire was to have gone into effect.
But Hamas said it was Israel which violated the truce.
"It is the occupation which violated the ceasefire. The Palestinian resistance acted based on... the right to self-defense (and) to stop the massacres of our people," spokesman Fawzi Barhum said in a statement.
NJF/NJF