The national football federation said in a statement that Saturday's match would be held in the central town of Elbasan instead of the northern town of Shkodra.
The state prosecutor in Tirana refused to confirm a report in the local Panorama newspaper of plans for a terror strike during the match.
But a source at the Israel Football Association in Jerusalem told AFP that they were asked about moving the game over concerns of an attack.
"The Albanians called us and FIFA and informed both sides about some information they had about possibility of a terror attack. They asked if it is ok by us to move the game from Shkodra to Elbasan," the source said, declining to be named.
"We of course contacted our security forces and intelligence before taking that kind of decision. They checked it and said it was ok".
Police in Albania detained four people on Saturday on suspicion of financing terrorism, recruiting Islamic State fighters for Syria and spreading "terrorist propaganda".
According to the unconfirmed Panorama report, the four suspects, including a doctor and hairdresser from Shkodra, were planning to obtain explosives for attacks before and during Saturday's match.
The prosecutor's office said that the suspects had regularly visited a radical mosque in a Tirana suburb, which was closed last year, and recently attended the trial of a group of radical imams accused of advocating terrorism.
They were arrested in a crackdown that also led to the detention of nine people in neighbouring Kosovo.
In Pristina, a source in the prosecutor's office told AFP on Tuesday that the group planned "attacks on institutions and vital buildings in Kosovo," adding that they had "no information" on a planned attack in Albania.
Albania, home to around three million people, is a predominantly Muslim country where the vast majority practise a moderate form of Islam. But radical fringes have been on the rise in recent years following the wars in Syria and Iraq.
From 2012 to 2014, between 100 and 120 Albanians joined the ranks of jihadists abroad, according to authorities.
About 15 Albanians have been killed in Syria or Iraq, and around 30 have returned home.