Reporting from Amman on Friday, she said: "We've heard of the Jordanian authorities arresting a cab driver on suspicion that he had planted the roadside bomb."
She said there was speculation that a "professional terrorist cell " was responsible for the attack.
"Security officials from Jordan and Israel has speculated that there might be a group affiliated to al-Qaeda or a Palestinian group," El-Shamayleh said.
"The attack exposes some kind of security breach. Israeli diplomats in Jordan are not allowed to use the highway that leads to the Allenby Bridge without being escorted by heavy security from both countries.
"But we know no other vehicles were accompanying the Israeli diplomats travelling in the car."
Jordan signed a peace treaty with Israel in 1994 - the second Arab state to do so after Egypt.
However, the treaty is widely rejected by the Jordanian population. Up to 60 per cent of Jordan's population is of Palestinian origin.
Our correspondent said that while security co-operation and other kinds of co-ordination are continuing between the countries' leaderships, the relations between Israel and Jordan are becoming cooler.
"The population at large widely rejects the peace treaty and believes it has not brought them anything, especially that there is no solution for the Palestinian conflict."
The bridge which links Jordan to the West Bank is located 50km from Amman. It is called Allenby in Israel and King Hussein Bridge on the Jordanian side.