The soldier, named as Hadar Goldin, 23, went missing when Israeli forces trying to destroy a suspected militant tunnel were attacked, Israel's military said, reports BBC.
Hamas has not commented on the latest reported capture.
In 2006 Palestinian militants captured Israeli soldier Gilad Shalit and held him for five years.
He was released in November 2011 in exchange for 1,000 Palestinian prisoners.
Gaza truce with Hamas collapsed just hours after it began, the report said.
Israel and Hamas accused each other of breaching the 72-hour ceasefire.
At least 35 people were killed by Israeli shelling in the southern town of Rafah, Palestinian sources said.
Some 1,460 Palestinians, mostly civilians, have died in the latest conflict and 63 Israelis, mostly soldiers.
