Experts were combing the area where he was last seen for clues, said Western Cape police spokesperson FC van Wyk.
He said Parker, 65, was allegedly kidnapped by five unknown males around 09:10 at his business in Fairway Close on Monday.
A double cab light delivery vehicle had followed Parker as he was driving into the basement.
The armed men apparently forced the security guard at the gate into the toilet cubicle, where they took his cellphone and locked him up.
“They then continued into the basement where they forced the businessman into their vehicle and drove off in an unknown direction.”
Cases of armed robbery and kidnapping were being investigated.
Parker is a founding member of the Food Property Group.
He is a board member of Al-Amien Foods and a non-executive board member of Brimstone Investment.
Family spokesperson and attorney Walid Brown said they would be releasing a brief statement later on Tuesday.
Jamiatul Ulama, the South Africa Council of Muslim Theologians, expressed concern at another apparent kidnapping.
“There has been a spate of kidnappings over the past two years. As such, our community is troubled and concerned by such suspected cases of kidnapping, which were once rare, but [are] now seemingly taking a pattern,” said its secretary general Ebrahim Bham.
He said Parker’s disappearance followed that of another prominent businessman and community member, Shiraz Gattoo, who had been missing since March 10.
“We have been made to understand that a Durban-based businessman was also kidnapped a few weeks ago and is still missing.”
Just under a year ago, on July 25, 2017, three armed men kidnapped Sadeck Zhaun Ahmed, who owns Zhauns Business Opportunity Machines in Woodstock, Cape Town.
He was eventually released at the end of August.
Muslim Judicial Council spokesperson Mishka Daries said that they had sent their sympathies to the Parker family and his colleagues.
“The family though has decided to deal with the tragedy privately. We respect their request but will avail ourselves when (if) they need our assistance,” she said.
“We continue to pray for Mr Parker’s safe return and appeal to the authorities to do everything in their power to find him swiftly.”
Jamiatul Ulama appealed to the police and law enforcement agencies to prioritise these cases “in order to stymie any criminal elements that are involved in kidnappings”.
“We pray for the safety of the kidnapped community members so that they can return and reunite with their families,” said Bham. DM
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