Israeli Prime Minister Benjamin Netanyahu and the military have yet to comment on the announcement.
"The question asked is why now", Lieberman said at a press conference on Wednesday. The opposition parties joined his call.
Liberman's resignation follows months of speculation about whether the prime minister will dissolve the government and move up elections, now scheduled for November 2019.
Hamas said that Lieberman's resignation is a recognition of Israel's defeat in this week's military confrontation with the Islamic group.
Sirens wailed in southern Israel as militants unleashed barrages of rocket and mortar fire, sending residents rushing to shelters. Hamas, in turn, had scaled back its mass protests that have led to weekly bloodshed along the Israeli border. "But in times of crisis, when making critical decisions in the field of security, the public can not always be a partner in the crucial considerations that must be concealed from the enemy".
"I see the big picture of Israeli security that I can not share with the public", he said.
Netanyahu claimed that Palestinian group Hamas "begged" for a cease-fire, saying "they know very well why". I can not detail our plans for the future.
The government formed after 2015 elections was already seen as the most right-wing in Israel's history even before Lieberman joined.
"In times like these, leadership is not doing the easy thing. We will dictate the times and circumstances that are right for Israel and are right for the security of our people", Netanyahu said.
But he would want to make the move at the most advantageous time and he is now facing criticism over the Gaza ceasefire.
Hamas called the resignation of Israel's defense minister a "political victory for Gaza".
So while the cease-fire holds with Gaza, Netanyahu's government may not last the night.
Netanyahu has preferred to contain Hamas rather than seek to remove it from power, anxious that it would leave a power vacuum in Gaza and that Israel would have difficulty assuming security responsibility for the territory it withdrew from in 2005.
The Egyptian-brokered truce was announced by Gaza militant groups, including Hamas, on Tuesday.
Israel's agreement to a ceasefire after this week's escalation over Gaza has prompted protests in Israel among those demanding a harsher blow against Hamas.
On Wednesday, a Palestinian was shot and captured by the Israeli military after being discovered hurling grenades across a perimeter fence. Reuters says Israeli troops have killed around 220 Palestinians. Some 26 other people were wounded in the Palestinian territory, according to Gaza's health ministry.
Palestinian U.N. Ambassador Riyad Mansour told reporters at U.N. headquarters that "we are grateful for the Egyptians who are mediating". He also condemned the government's decision to send Qatari-bought fuel into Gaza.
Palestinians check on Tuesday the damage of a building destroyed by Israeli airstrikes in Gaza City.
"We are third-class citizens here in Sderot and the communities on the border with Gaza", complained David Maimon, a local resident.
"It only lets us suffer, nothing more".
