The armed forces said the operation on Monday was conducted in co-ordination with Damascus in retaliation for an attack on a church in the US-allied country that killed nine people on Friday.
It said the operation "resulted in the killing and wounding of many members of these terrorist groups and the destruction of a number of their vehicles." It did not specify who the groups were or the precise location of the strikes.
There was no immediate comment from Syrian authorities. Five civilians, including women and children, were killed as a result of the Jordanian strikes, a health official told Syria's state news agency.
There was no immediate comment from Jordan on that account.
Hours earlier, senior government security officials said their security forces had arrested two brothers and their brother-in-law after a shootout on Monday over the church violence that killed nine people.
"God willing, they only represent themselves," said Jordan's Director of Public Security, Major-General Obeidallah al-Maaytah.
Such violence is highly unusual in Jordan, a relatively stable US ally in the Middle East. Friday's attack on the Christian minority prompted King Abdullah to order security forces to respond with an "iron fist".
In a press conference, al-Maaytah and Interior Minister Mazen al-Faraya said the country would not tolerate extremist terrorism.
"The file has not yet been closed; investigations are still ongoing. As of today, there are no indications of any links between them and other cells," al-Faraya added.
Friday's assault during a funeral at a Greek Orthodox church in the village of Hamoud, about 120km southwest of the capital, Amman, also wounded at least 34 people.
Witnesses said gunmen opened fire for several minutes. The suspects, who lived near Hamoud, will face justice, said the security officials. The three suspects were named in the press briefing.
Reuters video footage showed a building pockmarked by the exchange of fire in the village of al-Judayyda, in Karak governorate.
Jordan's Public Security Directorate said in a statement carried by state media that security forces located the suspects while they were hiding in an abandoned house. They refused to surrender and attacked security forces, who returned fire and arrested all three after wounding them.
No security personnel were injured, and security forces found a number of firearms and rounds of ammunition in the suspects' possession.
There has been no claim of responsibility for the church attack.
Jordan, a US partner in the fight against extremism, has foiled Islamist militant plots in the past. The security officials did not name any Islamist groups in the press conference.
with AP
