A statement from the Shin Bet did not give the number or identities of suspects or say if any had been arrested or charged but said that the alleged Iranian-run operation was discovered "in recent months."
"The network was based in Syria under Iranian guidance and was led by a Syrian operative nicknamed 'Abu Jihad'", it said.
"It attempted to recruit people via preliminary contacts based on fictitious Facebook profiles and - later - messaging apps."
"The affair joins other recent events in which terrorist elements (including those from Hamas and Hizballah) have established contacts with Israeli Arabs and Palestinians over the internet in order to recruit them for intelligence gathering and terrorist activity," the statement added.
It said that those contacted were asked to gather data on sites such as military bases and police stations with a view to providing Iran with potential Israeli targets.
"The decisive majority of Israeli citizens refused to cooperate," it added.
Israel's Arab minority - who number more than 1.3 million - are the descendents of Palestinians who stayed on their land when the state of Israel was established in 1948.
Israel considers Iran its archfoe and has carried out hundreds of strikes in neighbouring Syria against what it says are Iranian and Hezbollah military targets.
It has vowed to keep Iran from entrenching itself militarily there.
On Sunday Israeli cabinet minister Tzachi Hanegbi boasted on public radio how his country had been killing Iranians for the past two years.
"We strike the Iranians hundreds of times in Syria," he said in an interview. "Sometimes we acknowledge it and sometimes foreign reports reveal it."
Syria's state news agency said that Israel fired missiles at Syrian military positions held by the government and its allies early on Wednesday.
The missiles were fired into southern Syria, close to the Israeli-occupied Golan Heights. Israel's military declined comment.
Last month Israeli military prosecutors charged a Palestinian-Jordanian accused of working to set up Iranian spy networks in the Jewish state and the occupied West Bank.
In 2018 Israel charged three Palestinians with planning "terrorist" attacks on behalf of Iran, and in 2015 an Israeli court sentenced an Iranian-born Belgian citizen to seven years in prison for spying for Tehran while posing as a businessman.
