Mr Bitton, who was born in Ashdod, has previously spoken of his frustration at the abuse he receives from Celtic fans because he is an Israeli.
In 2016 he wrote on his Instagram that the trolls were "nothing but idiots" and said they accused him of supporting the killing of children.
“I’m all up for the banter but not when you guys texting my wife’s Instagram," he said.
He continued: “As a father if you guys think I support the death of children or any human being then you are nothing but idiots!!!
“I’m getting abuse for a while so I just felt that I had to say that. Don’t mix football and politics, you are better than that."
Celtic fans had displayed an “end Zionism” banner in May 2016 during the Scottish FA Cup final in Glasgow.
The club has previously been disciplined by Uefa for similar gestures, with fans regularly holding Palestinian flags aloft at matches in a sign of their hatred of Israel.
Police also launched an investigation in August 2016 after another Celtic fan said gassing was “too good” for the club’s Israeli midfielder.
Student Daniel Yahia also described Bitton as “a filthy Zionist rat” and claimed: “Zionists are subhuman.”
One of Yahia’s friends, who called himself Podge Mullan, then suggested that Bitton should be “gassed”.
Yahia replied: “Be too good for him mate.
“Expose him to the worst torture the Israeli Defence Force uses on young Palestinian kids, see how much of a man he is then. Scumbag.”
In November 2015, Celtic director Lord Livingston, a Conservative member of the House of Lords, was also targeted with antisemitic abuse by Celtic fans.
The former Minister for Trade received the abuse after voting against delaying £4.4bn worth of government cuts.
He said he had received a message from someone under the name Michael Higgins who had said: “Get this Ashkenazi c*** out of OUR club and take that other fake jew p**** [Celtic’s Israeli midfielder Nir] Bitton with him. This is typical of their sort, infiltrating and destroying every country and establishment from within”.
Another person writing as ‘Ross Grant’ had told him: “He’s a Jew what do you expect”.
Mr Bitton was shown a straight red card on Sunday after he was judged to have denied a goal scoring opportunity when he brought down Rangers' Alfredo Morelos in the 62nd minute of the crunch Premiership tie.
The JC has approached Celtic FC for comment over the antisemitic abuse sent to Mr Bitton.
