The 32-year-old woman had been diagnosed with the deadly coronavirus last month when she was eight months pregnant.
So far her newborn son has not tested positive for the disease but the World Health Organisation said "further investigations into close contacts of the family, the newborn baby and healthcare workers are ongoing."
However both her 38-year-old husband and their elder son, eight, have been diagnosed as being infected.
"The condition of both husband and son is currently stable and they are receiving the required care," state news agency WAM reported late Monday.
The WHO said the elder son had "mild respiratory symptoms" and was being kept in isolation in hospital.
The WHO says it has been informed of 163 laboratory-confirmed cases of MERS worldwide since September last year, including 70 deaths.
Saudi Arabia is by far the worst affected country, accounting for 55 deaths out of 130 confirmed cases.
Experts are struggling to understand the MERS virus, for which there is no vaccine.
It is considered a deadlier but less-transmissible cousin of the SARS virus that erupted in Asia in 2003 and infected 8,273 people, nine percent of whom died.
In August, researchers pointed to Arabian camels as possible hosts of the virus.
But the Jordanian family infected in Abu Dhabi "had no travel history, no contact with a known confirmed case and no history of contact with animals," the WHO said.
Like SARS, MERS appears to cause a lung infection, with patients suffering from a temperature, cough and breathing difficulties.
But it differs in that it also causes rapid kidney failure and the extremely high death rate has caused serious concern.