Israeli media said the bomb detonated near the convoy taking Israeli ambassador to Jordan, Dani Nevo, to the bridge, also known as the Allenby, 50 kilometres (30 miles) west of Amman.
But sources in Jordan said it was former Israeli ambassador Yakov Rosen in the convoy, not Nevo, while Israel's foreign ministry said it was unclear whether Nevo was in the convoy headed to Israel via the West Bank.
Israel's YNet News said four embassy staff members and two security guards were in the convoy, while Haaretz newspaper said on its website that two remotely detonated bombs exploded, causing one car to flip over.
The embassy's consular officer and her husband arrived back in Israel, the country's state-run Channel One TV reported.
Jordan's information minister said there were no casualties or damage.
"While cars, including two Israeli embassy cars, were travelling near the town of Naur on the road between Amman and the Jordan Valley a bomb exploded without causing casualties or damage," Nabil Sharif told AFP.
"The cars were not damaged by the blast," Sharif said, adding that an investigation was under way into the attack and to determine the type of explosives used.
A source close to the investigation said: "The blast left a crater... 10 centimetres (four inches) deep and 80 centimetres (32 inches) wide."
An AFP photographer said police blocked all roads leading to the scene of the blast.
Israeli diplomats often travel home on Thursdays, the start of the Muslim weekend in Jordan, and return on Sundays to Jordan, which in 1994 became only the second Arab state to sign a peace treaty with Israel, after Egypt.
Israeli diplomats in Jordan usually use rental cars.
There have been several attacks or attempted attacks against Israelis in Jordan since the signing of the treaty but such incidents have been rare in recent years.
In 2003, a Jordanian driver crossed the southern border with Israel and opened fire at a group of foreigners in the transit zone. He was shot by Israeli soldiers.
A non-Israeli tourist was killed and five others were wounded.
Israeli analysts said there was excellent security coordination between Jordan and Israel, and that Amman had foiled several attempts to attack Israeli targets in the past.
"I'm sure this was a surprise for the Jordanians. These people are probably Islamic or Al-Qaeda that pose a danger to the Hashemite kingdom too," Ephraim Inbar, the director of the Begin-Sadat Centre for Strategic Studies, told AFP.
Jordan's Muslim Brotherhood said "such incidents should be expected."
"As long as Israel is in the region, carrying out its non-stop aggression against the Palestinian people, we should expect these things to happen," Brotherhood spokesman Jamil Abu Baker told AFP.
"Israel is the source of violence in the Middle East."
The influential Muslim Brotherhood and its political arm, the Islamic Action Front, have repeatedly called for the scrapping of the peace treaty, expulsion of Israel's ambassador and a cut in relations with the Jewish state.
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