"We've had some disagreements with the leader of the ruling party," Kvirikashvili said in a televised statement on Wednesday.
Ivanishvili is a former premier and the richest man in the ex-Soviet country.
"I think there is a moment now when the leader of the (ruling) party should be given an opportunity to staff a new cabinet," he added, Presstv reported.
Fifty-year-old Kvirikashvili has been in office since 2015. His resignation comes after the Georgian capital, Tbilisi, was hit by anti-government protests.
Georgians staged protests on May 31 against what they said was a miscarriage of justice following the murder of two teenagers in December. On June 9, the protests stopped, but resumed on June 10 and ended a day later with police removing the protesters' tents and arresting opposition politicians and their supporters.