The two were set to face-off on King Hussein/Allenby Bridge crossing between Jordan and the Israeli-occupied West Bank before the Israeli prime minister stepped in.
Prime Minister Benjamin Netanyahu stopped an Israeli lawmaker from taking on a Jordanian counterpart in a fist fight on Wednesday over a diplomatic crisis between the two neighbours.
The July 23 shooting to death of two Jordanians by an Israeli embassy guard who said he was acting in self-defence has outraged Amman, stirred up pro-Palestinian sentiment in the kingdom and prompted US mediation efforts.
Oren Hazan, a member of Netanyahu's rightist Likud party had tweeted on the day of the shooting that Jordanians "who we keep supplied with water and whose butts we defend day and night" needed "re-education."
His comments prompted a challenge from a similarly fiery lawmaker in Jordan. "Let him meet me, if he is a man," Yahya Soud said on Twitter.
They were due to square off against each other on Wednesday morning on the border.
As the appointed time neared, both men posted images of themselves on social media driving to the King Hussein/Allenby Bridge crossing between Jordan and the Israeli-occupied West Bank.
But Hazan's journey was cut short after Netanyahu's office ordered him to turn around. A statement from the prime minister's office did not say why Netanyahu had stopped the fight from proceeding.
There was no immediate comment from Jordan.
Hazan said on Twitter he was disappointed the encounter had not taken place.
Soud told reporters he had been "serious about going down to the bridge and busting this dirty man's nose". Netanyahu stepped in, Soud said, because Israelis "can't face up to Jordanians."
In 1994, Jordan became the second of only two Arab countries to make peace with Israel.