The Israeli military said they believe the soldier went missing during a continued operation to destroy tunnels used by militants to gain access into Israel from Gaza.
A statement from the Israel army said: "An attack was executed against IDF forces operating to decommission a tunnel. Initial indication suggests that an IDF soldier has been abducted by terrorists during the incident. The IDF is currently conducting intelligence efforts and extensive searches and in order to locate missing soldier."
An Israel Defence Forces spokesman said earlier on Twitter: "We are conducting extensive searches in S. Gaza in order to find a missing IDF soldier. We suspect the soldier was kidnapped by Hamas today."
Officials in Gaza say 27 Palestinians were killed by Israeli shelling just hours after the ceasefire began this morning.
Eight rockets and mortar bombs were fired from Gaza at Israel, the Israeli military said, adding that one was intercepted by the Iron Dome system and seven hit open areas.
The office of the Israeli Prime Minister Benjamin Netanyahu released a statement accusing Hamas of breaking the ceasefire, saying: "Once again, Hamas and the terror organisations in Gaza have blatantly broken the ceasefire to which they committed, this time before the American Secretary of State and the UN Secretary General."
The ceasefire was announced earlier in a joint statement by the US Secretary of State John Kerry and the UN Secretary-General Ban Ki-moon amid a rapidly climbing death toll since hostilities began July 8.
Palestinian officials say more than 1,499 Palestinians have been killed and nearly 7,000 wounded. Israel says 61 of its soldiers, two civilians and a Thai national have died and more than 400 have been injured.
Mr Kerry warned ahead of the truce it was “a respite, not an end” to the conflict.
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