The blast hit a security patrol in Al-Fuhais, 12 kilometres (8 miles) west of the capital on Friday evening, it said.
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"It killed Sergeant Ali Adnan Qawqaza and wounded six other members of the patrol," the ministry said, adding that an investigation was underway into the cause of the blast.
Security forces had been deployed to protect the town's annual festival, which hosts prominent Arab music acts.
Prime Minister Omar al-Razzaz vowed that Jordan would "not be complacent in the hunt for terrorists".
"Jordan will always be at the forefront of the fight against terrorism and obscurantist ideas which target the lives of innocents and try to undermine security and stability," he said in remarks carried by the official Petra news agency.
Jordan has played a key role in the US-led coalition fighting IS in neighbouring Syria and Iraq, using its air force and allowing coalition forces to use its bases.
The kingdom was hit by a string of jihadist attacks in 2016, including a suicide bombing in June that killed seven guards near the border with Syria that was claimed by IS.
Months later in December a shooting rampage, also claimed by IS, killed 10 people including a Canadian tourist.
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