Police swarmed the estates, blocking driveways and doorways and barring people from going out.
Victoria recorded 108 new virus cases on Saturday, including a cluster of up to 30 cases across a few housing estates.
The government's decision to lock down all nine towers was made because of "patterns of movement, friendship groups, family groups," the premier said.
He also cited the crowded living in public housing and many communal spaces, meaning community transmission was high risk.
Mr Ibrahim, a Somali-Australian who has lived in Australia for 10 years after fleeing his war-torn homeland, said he couldn't find out how to get his specific needs met.
His household supplies are low as he and his wife do their weekly shop on Sundays.
They need formula for the baby twins, nappies, milk, weetbix, soap, toothpaste, laundry powder, fruit, vegetables and meat.
"This is not fair," Mr Ibrahim told AAP.
"There are a lot of postcodes in lockdown but they are allowed to leave the house for essentials.
"What the Victorian government is doing is discriminating the people who don't have a voice.
"We are not different from the rest of the Victorian community which is in lockdown now."
Mr Ibrahim is a casual pick-packer in a warehouse in Melbourne's west and is not paid if he doesn't turn up.
He said the imprisonment imposed on him felt like he'd gone back in time to the trauma his family ran from.
The premier's office told AAP urgent requests for food and supplies were being triaged via Victoria Police and health department officials on site and interpreters are assisting.
The state government has financial support for those who cannot attend work because of home isolation.
People in Australia must stay at least 1.5 metres away from others. Check your state’s restrictions on gathering limits.
Testing for coronavirus is widely available across Australia. If you are experiencing cold or flu symptoms, arrange a test by calling your doctor or contact the Coronavirus Health Information Hotline on 1800 020 080.
The federal government's coronavirus tracing app COVIDSafe is available for download from your phone's app store.
SBS is committed to informing Australia’s diverse communities about the latest COVID-19 developments. News and information is available in 63 languages at sbs.com.au/coronavirus