The aircraft was forced to dump fuel before making a safe landing at Heathrow at around 11.10am Wednesday morning (local time).
The mother and her baby are believed to have been taken to hospital by emergency services.
Saudia is the national carrier of Saudi Arabia, with its main operational base at Jeddah-King Abdulaziz International Airport (JED).
The airline has a fleet of 163 aircraft and flies to 126 destinations around the world.
The journey time from Jeddah to New York is at least 12 hours. The aircraft was seven-and-a-half hours into the journey before it had to land in London.
MailOnline has contacted Saudia and London Heathrow for comment. This is a developing story.
In April this year, a pregnant mother who unexpectedly went into labour on a flight from Singapore decided to name her baby boy "Jet Star" after airline crew helped her safely deliver the infant on board.
Three doctors happened to be on Friday's three-hour flight to Myanmar and assisted the women in delivering the baby as the plane taxied at Yangon airport.
The mother's family name is Star and she decided to name her son "Saw Jet Star," because of the "care she received from the airline".
The airline offered the mother $1,000 worth of baby supplies and the three off-duty doctors were provided with flight vouchers.