The match was supposed to be Argentina's final "friendly" before the team travels to Russian Federation for the World Cup.
The cancellation followed protests in support of Palestinian rights. In Gaza, people cheered and in Ramallah in the West Bank, the Palestinian Football Association issued a statement thanking Messi and his colleagues for cancelling the game.
The match was cancelled on Wednesday scheduled to take place in Jerusalem.
The status of Jerusalem, always a key sticking point in the Israeli-Palestinian dispute, surged back to centre-stage when Trump tore up decades of United States policy to recognise it as Israel's capital in December.
Pro-Palestinian activists protested in front of the sports complex where Lionel Messi and the rest of the Argentina squad are preparing on Tuesday.
Claudio Tapia, president of the AFA, apologised for cancelling the match but said the safety of the players was at stake.
Israeli media said that late Tuesday Prime Minister Benjamin Netanyahu called Argentine President Mauricio Macri, with whom he has good relations, in an effort to save the match but that Macri had said he was unable to intervene.
Israeli defense minister Avigdor Lieberman said, "It's unfortunate the soccer knights of Argentina did not withstand the pressure of the Israeli-hating inciters". "We will not yield before a pack of anti-Semitic terrorist supporters".
Palestinian football officials praised Argentina and its star Lionel Messi on Wednesday for calling off a friendly match against Israel that Israeli officials had planned to move to Jerusalem. Rajoub has long attempted to get FIFA, football's world governing body, and the International Olympic Committee to take action against Israel. The stadium is located in a neighborhood which had once been an Arab village destroyed by Jewish militias in the 1948 Palestinian Nakba.
Rajoub had accused Israel of playing politics with the game by moving it from the port of Haifa to Jerusalem. The team responded to creative campaigning from fans around the world denouncing Israel's sports-washing of its crimes against Palestinians. He said, "They tried to use sport as a tool for political ends, and for this I think, they failed". Israeli President Reuven Rivlin said in a statement "the politicisation of Argentina's move is very worrying".
MK Itzik Shmuli, also of Zionist Union, said that "even her fury, slander and sowing hatred won't hide the truth. You politicize it once with Israel, then you politicize it for everyone, and it will cause the deterioration of a great institution".
Israel has not qualified for the tournament. Jerusalem was invaded and occupied in 1967 by Israel, which wants all of the city as its capital. Labor Party leader Avi Gabbay called for a police investigation into Regev's "corrupt conduct".
"Not that we needed it but it again showed how the management of Argentine football is a huge mafia", said Lorena Quiroga, a 40-year-old small business owner. "This is not just sports", he tweeted.
Ofer Eini, President of the Israeli Football Association (IFA), and Rotem Kamer (R), CEO of the Israeli football Association, take part in a press conference on June 6, 2018, in the Israeli town of Ramat Gan, east of Tel Aviv, to announce that the IFA will file a formal complaint to FIFA, against the Palestinian Football Association, following the cancellation of the game between the Israeli and Argentina.