Defence minister Avigdor Lieberman issued the order to prevent the diplomats from travelling to the Palestinian enclave from Israeli territory, the official said on condition of anonymity.
The order will remain in place "until clarifications occur," said the official, without providing further details.
Israel controls all access into Gaza apart from the strip's sole crossing with Egypt.
On Tuesday, Switzerland's envoy to the Palestinian Authority, Julien Thoni, met Hamas's chief in the Gaza Strip, Yahya Sinwar.
At least one other recent meeting was also held with Hamas leaders.
Hamas, the Islamist movement that has controlled the Gaza Strip for a decade, is considered a terrorist organisation by the United States and European Union.
It has fought three wars with Israel since 2008.
Switzerland however has contacts with Hamas in order to maintain dialogue with all parties to the Israeli-Palestinian conflict as part of its peace and human rights efforts.
Israel's army radio reported that the decision to bar them from Gaza was taken due to the public nature of the meetings, with Hamas posting photos on its website.
The meetings come with Hamas due to hand over power in Gaza to the Palestinian Authority by Friday as part of a landmark reconciliation deal signed in October.
There are however doubts over whether a significant transfer of power will occur by that time.