The 65-year-old is the founding member of the Foodprop Group, which owns the Foodworld chain of stores.
Muslim Judicial Council spokesperson Mishka Darries said the organisation was still deeply concerned that Parker had not been found yet.
The council made contact with police last month about Parker after it noted a trend of Muslim businessmen being kidnapped.
When Independent Media contacted family spokesperson Walid Brown, he said he was not in the country, but said there were no new updates.
According to police, Parker was taken when he was driving into the basement parking of his business premises in Parow. A double-cab bakkie followed him and at the gate, the suspects forced the security guard into the toilet at gunpoint, took his cellphone and locked him up.
They then forced Parker into the car and drove off.
Police confirmed that the case was being investigated by provincial detectives.
Parker’s was the latest in a string of kidnappings in recent years after Sadeck Zhaun Ahmed was taken from his business last year.
The 71-year-old owner of Zhauns Business Opportunity Machines was kidnapped in Woodstock on July 25, last year, by three men who threatened him with a firearm.
Since 2016 three other businessmen have been kidnapped.
Last September an unidentified businessman from Monte Vista was kidnapped while in October 2016, Naushad Deshmukh Khan was taken from his clothing shop in Athlone by a group of armed men. Allegedly R9.7 million was paid for his release about two months after he was taken.
Mustapha Goolam, owner of Foodtown Supermarket, was taken from his business in Lotus River in December 2016 when two men attacked him and forced him into a car.
The kidnappers demanded a ransom of R10m but Goolam was released two days later.
Cape Chamber of Commerce president Janine Myburgh said that while the kidnappings didn’t necessarily represent a trend, they could have negative impacts on the city.
“If being a successful businessman in Cape Town puts you at risk, then it most definitely affects our image with less wealthy individuals wanting to live here. However, although one kidnapping is too much, five in two years is not necessarily a trend. In some South and Central American countries the number of kidnappings (that are reported) runs into the thousands per annum,” she said.
“Kidnapping is a crime, but one that makes for news and is widely publicised so it definitely has a disproportionate effect on our image.”