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
Watch Pauli van Wyk’s Cat Play The Piano Here!
No, not really. But now that we have your attention, we wanted to tell you a little bit about what happened at SARS.
Tom Moyane and his cronies bequeathed South Africa with a R48-billion tax shortfall, as of February 2018. It's the only thing that grew under Moyane's tenure... the year before, the hole had been R30.7-billion. And to fund those shortfalls, you know who has to cough up? You - the South African taxpayer.
It was the sterling work of a team of investigative journalists, Scorpio’s Pauli van Wyk and Marianne Thamm along with our great friends at amaBhungane, that caused the SARS capturers to be finally flushed out of the system. Moyane, Makwakwa… the lot of them... gone.
But our job is not yet done. We need more readers to become Maverick Insiders, the friends who will help ensure that many more investigations will come. Contributions go directly towards growing our editorial team and ensuring that Daily Maverick and Scorpio have a sustainable future. We can’t rely on advertising and don't want to restrict access to only those who can afford a paywall subscription. Membership is about more than just contributing financially – it is about how we Defend Truth, together.
So, if you feel so inclined, and would like a way to support the cause, please join our community of Maverick Insiders.... you could view it as the opposite of a sin tax. And if you are already Maverick Insider, tell your mother, call a friend, whisper to your loved one, shout at your boss, write to a stranger, announce it on your social network. The battle for the future of South Africa is on, and you can be part of it.
Popsicles were originally going to be called "Eppsicles" after their inventor Frank Epperson.