It is not clear who was behind the attack, which was launched from Syrian territory, close to a refugee camp.
The Jordanian government said no new refugee camps would be built and none would be expanded.
Dozens of people have taken part in a candlelit vigil in the capital, Amman, in memory of the victims.
Tuesday’s attack, the first of its kind since the conflict in Syria began in 2011, saw a truck full of explosives driven at high speed over the border from Syria and blown up beside a Jordanian military post.
“Any vehicle and personnel movement within these areas that move without prior coordination will be treated as enemy targets and dealt with firmly and without leniency,” an army statement said.
The order went into effect immediately.
Jordan’s Information Minister, Mohammed Momani, told the BBC there had been warnings for months that militants – including members of the so-called Islamic State group – were hiding among Syrians stuck at the borders.
He said Jordanians were angry at the attempt to undermine their country’s security and stability.
International relief workers said the Jordanian authorities had also suspended all humanitarian aid to the area, and warned that this could put the lives of refugees at risk.
Tens of thousands of Syrians who have been trying to enter Jordan are currently staying in this remote area of the desert.