The attack, which took place in Baqaa, the country's largest refugee camp, is understood to be the work of a lone attacker and saw the death of three intelligence officers and two workers, Petra reported, citing government spokesman Mohammed al-Momani.
The camp is a vast facility housing some 120,000 Palestinian refugees situated about 20 kilometers (more than 12 miles) from the capital, Amman.
Al-Momani said the initial indications are that this was an individual isolated incident and that the investigation is still ongoing.
A single assailant armed with an automatic weapon was responsible, reported Al Rai, a newspaper close to the government, citing "informed sources."
The attacker drove to the office at about 7 a.m. local time before carrying out the attack, the newspaper reported.
Describing it as a "terrorist" act, Momani said the targeting of the office on the first day of the holy month of Ramadan
showed "a clear indication of their criminal behavior and their deviation from our religion," according to Petra.
Authorities are searching for the attacker; there has been no claim of responsibility.
'Despicable act of terror'
Jordan's Queen Rania tweeted her condolences Monday.
"At the start of the month of giving and mercy, a despicable act of terror has taken the lives of five of Jordan's sons," she wrote on her official account.
"We offer our condolences to the nation on these martyrs of duty, and call on God to grant their families patience and solace."
Jordan is a key Arab member of the U.S.-led anti-ISIS coalition and has carried out strikes against the group in both Iraq and Syria.
In March, Jordanian security forces carried out a series of raids against suspected ISIS militants
it said planned to strike civilian and military targets in the country. Following the raids, seven suspected terrorists attacked Jordanian forces in the northern city of Irbid. All the militants and one Jordanian soldier died in the clash.
The Baqaa camp was established in 1968 for Palestinian refugees displaced in the 1967 Arab-Israeli War.