There was no immediate claim for the bombing but Jordan is a leading member of the US-led coalition fighting IS in neighbouring Syria and Iraq, and has been the target of extremist attacks in the past.
Fourteen soldiers were also wounded in the attack, a security official told AFP, adding that it was a "preliminary toll" and the number of dead might rise.
The army said the bomb struck at 5:30 am (0230 GMT) in Rukban, on the Syrian border in the far northeast of the kingdom.
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It said it destroyed several "enemy" vehicles at the border, but would give no further details until later in the day.
Foreign Minister Nasser Judeh condemned the "cowardly attack."
"Terrorists strike again this time against our border guard," he tweeted on his official account. "This evil will be defeated."
On June 6, a gunman killed five Jordanian intelligence officers in a Palestinian refugee camp north of the capital.
A suspect was later arrested but details of the attack have been kept under a gag order while the investigation continues.
Tens of thousands of Syrian refugees have sought shelter at two remote desert camps in the northeast -- one at Rukban and another at Handalat further west.
A flare-up in the five-year civil war in Syria sparked a new influx of refugees in the area last month, with nearly 5,500 arriving at Rukban within days in early May.
Jordanian authorities kept hundreds of refugees camped in no-man's land outside Rukban waiting for screening, out of fear that they are involved with IS which controls swathes of eastern Syria and neighbouring Iraq.
The kingdom's refusal to allow the refugees to move further inside Jordanian territory has drawn criticism from the office of the UN High Commissioner for Refugees.
Jordan says it is hosting nearly 1.4 million Syrian refugees, of whom 630,000 are registered with the United Nations.
The huge refugee presence has placed a massive strain on Jordan's economy and resources, and raised security concerns in a country which has already experienced several extremist attacks.
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In December 2005, suicide bombings in three Amman hotels claimed by IS's predecessor, Al-Qaeda in Iraq, killed 60 people and wounded dozens.
Jordan has carried out air strikes against IS in neighbouring Syria since 2014.
One of its pilots was captured by the militants when his plane went down in Syria in December 2014. In February 2015, IS released gruesome footage of Maaz al-Kassasbeh being burned alive in a cage.
His murder prompted Jordan to extend its air strikes against IS to Iraq, where it is the only Arab coalition member participating in the bombing campaign.
Jordan has also opened up the Prince Hassan airbase, northeast of the capital, to other members of the US-led coalition taking part in the air war.
In March, Jordanian authorities announced they had foiled an IS plot to carry out attacks in the kingdom in an operation that led to the deaths of seven militants.
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According to sources close to Islamists, almost 4,000 Jordanians have joined extremist groups in Iraq and Syria, where an estimated 420 have been killed since 2011.
The Baqaa refugee camp outside Amman, where the intelligence officers were shot dead earlier this month, was the home of Mahmud Abdelal, an extremist militant who blew himself up in Syria in October 2012.
In 2010, three Jordanian Islamist extremists were sentenced to prison terms of between three years and life for plotting to kill intelligence officers in the camp.
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