More snow could fall in some areas later this week, the forecasters said.
Overnight temperatures have occasionally dropped to 0°C this month and some snow fell in northern and southern regions, prompting authorities to delay working times by two hours in the morning as a precaution.
The official weather forecast said frost could form overnight and on Wednesday wind gusts could reach 70 kilometres an hour, with snow possibly falling at elevations above 700-800 metres.
Jordan has several regions of such altitude, in the north and south of the country and west of Amman.
“The kingdom will be affected by low-pressure weather situated over the Island of Cyprus. Temperatures will drop noticeably,” the weather forecast said.
“The weather will be turning cloudy and rain will be falling in the western parts, and bursts of hail will be occurring.
"Snow will fall according to the elevation."
Forecasters gave a warning about “the danger of lessened horizontal vision over high elevations due to fog" and “danger of vehicles slipping in areas that will be seeing rainfall”.
Temperatures in Amman are forecast to range between 0°C and 9°C for the rest of the week, with conditions remaining mild in the Jordan valley and the port city of Aqaba, where highs are expected to reach 18°C.
Parched Jordan has been hit by severe periods of drought over the past decade.
Official figures show that, so far this year, rainfall in most regions has been 50 per cent or lower, compared to the average for the rain season, which runs from November to March.
The main rain-fed farming region in the north has had 150 millimetres of rain so far this season, compared with a 400-millimetre average by the end of winter.
Southern desert areas near the border with Saudi Arabia have received 17 millimetres on average, compared with the 56 millimetres usually recorded by the end of the season.
But officials say improved rainfall in the last few weeks helped to replenish some dams, with at least one reservoir in central Jordan having run dry.
Illegal digging of wells for irrigation has also been a factor behind the depletion Jordan’s water table. Officials say some aquifers in desert areas have run dry because of illegal farming.