Culverwell and Nohai were arrested at the hospital for not being able to provide marriage certificates.
They were first taken to Yas Police Station, and then later brought to Al Wathba Prison.
They have not, however, been charged because authorities are still investigating the paternity of the child, how long the couple was sexually active and are testing Nohai's HIV status.
The couple had become engaged just two days before their arrest, on January 27.
Culverwell has been working in the UAE for the past five years as a water rescue operative at Yas Waterworld.
He first started dating Nohai, who worked as an administration officer, in mid-2014.
South Africa's Foreign Ministry said that it cannot help the couple because it is an issue with domestic UAE law, according to News24, and have suggested they seek legal help.
Culverwell's mother, Linda, said that Nohai was still in the early stages of her pregnancy, and suggested that the cramps could be a sign of a miscarriage.
She has pleaded for their release, saying that "the only thing they did wrong was fall in love".
Linda described her son as a health fanatic who didn't smoke, take drugs or drink alcohol.
She told News24 that her family is "trying to get messages to the two to say we love them and they shouldn't be worried".
Linda said that since the couple's arrest, family members and friends have been unable to contact them.
She said that the only people who can visit the couple are family members who share the same last name, and relatives are currently calculating the costs of making a trip to Abu Dhabi with lawyers.
Since their arrest, a Christian Church in Yas Island, UAE offered to marry the couple for a lofty price, but a judge refused to allow it, according to Herald Live.
Nohai is guilty of 'Zina', the Islamic legal term referring to unlawful sexual intercourse, which the UAE has criminalised.
Women and couples found guilty of Zina in UAE, women and couples are either deported or imprisoned in the country for at least a year.
Hundreds of women are imprisoned each year for the crime, including pregnant women and rape victims.